There are 230space groups in three dimensions, given by a number index, and a full name inHermann–Mauguin notation, and a short name (international short symbol). The long names are given with spaces for readability. The groups each have apoint group of the unit cell.

InHermann–Mauguin notation, space groups are named by a symbol combining thepoint group identifier with the uppercase letters describing thelattice type. Translations within the lattice in the form ofscrew axes andglide planes are also noted, giving a complete crystallographic space group.

These are theBravais lattices in three dimensions:

• P primitive
• I body centered (from the GermanInnenzentriert)
• F face centered (from the GermanFlächenzentriert)
• A centered on A faces only
• B centered on B faces only
• C centered on C faces only
• R rhombohedral

A reflection planem within the point groups can be replaced by aglide plane, labeled asa,b, orc depending on which axis the glide is along. There is also then glide, which is a glide along the half of a diagonal ofa face, and thed glide, which is along a quarter of either a face or space diagonal of the unit cell. Thed glide is often called the diamond glide plane as it features in thediamond structure.

• ${\displaystyle a}$,${\displaystyle b}$, or${\displaystyle c}$: glide translation along half the lattice vector of this face
• ${\displaystyle n}$: glide translation along half the diagonal of this face
• ${\displaystyle d}$: glide planes with translation along a quarter of a face diagonal
• ${\displaystyle e}$: two glides with the same glide plane and translation along two (different) half-lattice vectors.^{[note 1]}

A gyration point can be replaced by ascrew axis denoted by a number,n, where the angle of rotation is${\displaystyle \frac{{360}^{\circ }}{n}}$. The degree of translation is then added as a subscript showing how far along the axis the translation is, as a portion of the parallel lattice vector. For example, 2₁ is a 180° (twofold) rotation followed by a translation of⁠1/2⁠ of the lattice vector. 3₁ is a 120° (threefold) rotation followed by a translation of⁠1/3⁠ of the lattice vector. The possible screw axes are: 2₁, 3₁, 3₂, 4₁, 4₂, 4₃, 6₁, 6₂, 6₃, 6₄, and 6₅.

Wherever there is both a rotation or screw axisn and a mirror or glide planem along the same crystallographic direction, they are represented as a fraction$\frac{n}{m}$ orn/m. For example, 4₁/a means that the crystallographic axis in question contains both a 4₁ screw axis as well as a glide plane alonga.

InSchoenflies notation, the symbol of a space group is represented by the symbol of corresponding point group with additional superscript. The superscript doesn't give any additional information about symmetry elements of the space group, but is instead related to the order in which Schoenflies derived the space groups. This is sometimes supplemented with a symbol of the form${\displaystyle {\mathrm{\Gamma }}_x^y}$ which specifies the Bravais lattice. Here${\displaystyle x\in \{t,m,o,q,rh,h,c\}}$ is the lattice system, and${\displaystyle y\in \{\mathrm{\varnothing },b,v,f\}}$ is the centering type.^[2]

InFedorov symbol, the type of space group is denoted ass (symmorphic ),h (hemisymmorphic), ora (asymmorphic). The number is related to the order in which Fedorov derived space groups. There are 73 symmorphic, 54 hemisymmorphic, and 103 asymmorphic space groups.

The 73 symmorphic space groups can be obtained as combination of Bravais lattices with corresponding point group. These groups contain the same symmetry elements as the corresponding point groups. Example for point group 4/mmm (${\displaystyle \frac{4}{m}\frac{2}{m}\frac{2}{m}}$): the symmorphic space groups are P4/mmm (${\displaystyle P\frac{4}{m}\frac{2}{m}\frac{2}{m}}$,36s) and I4/mmm (${\displaystyle I\frac{4}{m}\frac{2}{m}\frac{2}{m}}$,37s).

The 54 hemisymmorphic space groups contain only axial combination of symmetry elements from the corresponding point groups. Example for point group 4/mmm (${\displaystyle \frac{4}{m}\frac{2}{m}\frac{2}{m}}$): hemisymmorphic space groups contain the axial combination 422, but at least one mirror planem will be substituted with glide plane, for example P4/mcc (${\displaystyle P\frac{4}{m}\frac{2}{c}\frac{2}{c}}$,35h), P4/nbm (${\displaystyle P\frac{4}{n}\frac{2}{b}\frac{2}{m}}$,36h), P4/nnc (${\displaystyle P\frac{4}{n}\frac{2}{n}\frac{2}{c}}$,37h), and I4/mcm (${\displaystyle I\frac{4}{m}\frac{2}{c}\frac{2}{m}}$,38h).

The remaining 103 space groups are asymmorphic. Example for point group 4/mmm (${\displaystyle \frac{4}{m}\frac{2}{m}\frac{2}{m}}$): P4/mbm (${\displaystyle P\frac{4}{m}\frac{2_1}{b}\frac{2}{m}}$,54a), P4₂/mmc (${\displaystyle P\frac{4_2}{m}\frac{2}{m}\frac{2}{c}}$,60a), I4₁/acd (${\displaystyle I\frac{4_1}{a}\frac{2}{c}\frac{2}{d}}$,58a) - none of these groups contains the axial combination 422.

Triclinic Bravais lattice

Triclinic crystal system

Number	Point group	Orbifold	Short name	Full name	Schoenflies	Fedorov	Shubnikov	Fibrifold
1	1	${\displaystyle 1}$	P1	P 1	${\displaystyle {\mathrm{\Gamma }}_t{C}_1^1}$	1s	${\displaystyle (a/b/c)\cdot 1}$	${\displaystyle (\circ )}$
2	1	${\displaystyle \times }$	P1	P1	${\displaystyle {\mathrm{\Gamma }}_t{C}_i^1}$	2s	${\displaystyle (a/b/c)\cdot \tilde{2}}$	${\displaystyle (2222)}$

Monoclinic Bravais lattice

Simple (P)	Base (C)

Monoclinic crystal system

Number	Point group	Orbifold	Short name	Full name(s)		Schoenflies	Fedorov	Shubnikov	Fibrifold (primary)	Fibrifold (secondary)
3	2	${\displaystyle 22}$	P2	P 1 2 1	P 1 1 2	${\displaystyle {\mathrm{\Gamma }}_m{C}_2^1}$	3s	${\displaystyle (b:(c/a)):2}$	${\displaystyle (2_0{2}_0{2}_0{2}_0)}$	${\displaystyle ({\ast }_0{\ast }_0)}$
4			P21	P 1 21 1	P 1 1 21	${\displaystyle {\mathrm{\Gamma }}_m{C}_2^2}$	1a	${\displaystyle (b:(c/a)):2_1}$	${\displaystyle (2_1{2}_1{2}_1{2}_1)}$	${\displaystyle (\overline{\times }\overline{\times })}$
5			C2	C 1 2 1	B 1 1 2	${\displaystyle {\mathrm{\Gamma }}_m^b{C}_2^3}$	4s	${\displaystyle \left(\frac{a+b}{2}/b:(c/a)\right):2}$	${\displaystyle (2_0{2}_0{2}_1{2}_1)}$	${\displaystyle ({\ast }_1{\ast }_1)}$,${\displaystyle (\ast \overline{\times })}$
6	m	${\displaystyle \ast }$	Pm	P 1 m 1	P 1 1 m	${\displaystyle {\mathrm{\Gamma }}_m{C}_s^1}$	5s	${\displaystyle (b:(c/a))\cdot m}$	${\displaystyle [{\circ }_0]}$	${\displaystyle (\ast \cdot \ast \cdot )}$
7			Pc	P 1 c 1	P 1 1 b	${\displaystyle {\mathrm{\Gamma }}_m{C}_s^2}$	1h	${\displaystyle (b:(c/a))\cdot \tilde{c}}$	${\displaystyle ({\overline{\circ }}_0)}$	${\displaystyle (\ast :\ast :)}$,${\displaystyle (\times {\times }_0)}$
8			Cm	C 1 m 1	B 1 1 m	${\displaystyle {\mathrm{\Gamma }}_m^b{C}_s^3}$	6s	${\displaystyle \left(\frac{a+b}{2}/b:(c/a)\right)\cdot m}$	${\displaystyle [{\circ }_1]}$	${\displaystyle (\ast \cdot \ast :)}$,${\displaystyle (\ast \cdot \times )}$
9			Cc	C 1 c 1	B 1 1 b	${\displaystyle {\mathrm{\Gamma }}_m^b{C}_s^4}$	2h	${\displaystyle \left(\frac{a+b}{2}/b:(c/a)\right)\cdot \tilde{c}}$	${\displaystyle ({\overline{\circ }}_1)}$	${\displaystyle (\ast :\times )}$,${\displaystyle (\times {\times }_1)}$
10	2/m	${\displaystyle 2\ast }$	P2/m	P 1 2/m 1	P 1 1 2/m	${\displaystyle {\mathrm{\Gamma }}_m{C}_{2h}^1}$	7s	${\displaystyle (b:(c/a))\cdot m:2}$	${\displaystyle [2_0{2}_0{2}_0{2}_0]}$	${\displaystyle [\ast 2\cdot 22\cdot 2)}$
11			P21/m	P 1 21/m 1	P 1 1 21/m	${\displaystyle {\mathrm{\Gamma }}_m{C}_{2h}^2}$	2a	${\displaystyle (b:(c/a))\cdot m:2_1}$	${\displaystyle [2_1{2}_1{2}_1{2}_1]}$	${\displaystyle (22\ast \cdot )}$
12			C2/m	C 1 2/m 1	B 1 1 2/m	${\displaystyle {\mathrm{\Gamma }}_m^b{C}_{2h}^3}$	8s	${\displaystyle \left(\frac{a+b}{2}/b:(c/a)\right)\cdot m:2}$	${\displaystyle [2_0{2}_0{2}_1{2}_1]}$	${\displaystyle (\ast 2\cdot 22:2)}$,${\displaystyle (2\overline{\ast }2\cdot 2)}$
13			P2/c	P 1 2/c 1	P 1 1 2/b	${\displaystyle {\mathrm{\Gamma }}_m{C}_{2h}^4}$	3h	${\displaystyle (b:(c/a))\cdot \tilde{c}:2}$	${\displaystyle (2_0{2}_{0}22)}$	${\displaystyle (\ast 2:22:2)}$,${\displaystyle (22{\ast }_0)}$
14			P21/c	P 1 21/c 1	P 1 1 21/b	${\displaystyle {\mathrm{\Gamma }}_m{C}_{2h}^5}$	3a	${\displaystyle (b:(c/a))\cdot \tilde{c}:2_1}$	${\displaystyle (2_1{2}_{1}22)}$	${\displaystyle (22\ast :)}$,${\displaystyle (22\times )}$
15			C2/c	C 1 2/c 1	B 1 1 2/b	${\displaystyle {\mathrm{\Gamma }}_m^b{C}_{2h}^6}$	4h	${\displaystyle \left(\frac{a+b}{2}/b:(c/a)\right)\cdot \tilde{c}:2}$	${\displaystyle (2_0{2}_{1}22)}$	${\displaystyle (2\overline{\ast }2:2)}$,${\displaystyle (22{\ast }_1)}$

Orthorhombic Bravais lattice

Simple (P)	Body (I)	Face (F)	Base (A or C)

Orthorhombic crystal system

Number	Point group	Orbifold	Short name	Full name	Schoenflies	Fedorov	Shubnikov	Fibrifold (primary)	Fibrifold (secondary)
16	222	${\displaystyle 222}$	P222	P 2 2 2	${\displaystyle {\mathrm{\Gamma }}_o{D}_2^1}$	9s	${\displaystyle (c:a:b):2:2}$	${\displaystyle (\ast 2_0{2}_0{2}_0{2}_0)}$
17			P2221	P 2 2 21	${\displaystyle {\mathrm{\Gamma }}_o{D}_2^2}$	4a	${\displaystyle (c:a:b):2_1:2}$	${\displaystyle (\ast 2_1{2}_1{2}_1{2}_1)}$	${\displaystyle (2_0{2}_0\ast )}$
18			P21212	P 21 21 2	${\displaystyle {\mathrm{\Gamma }}_o{D}_2^3}$	7a	${\displaystyle (c:a:b):2}$${\displaystyle 2_1}$	${\displaystyle (2_0{2}_0\overline{\times })}$	${\displaystyle (2_1{2}_1\ast )}$
19			P212121	P 21 21 21	${\displaystyle {\mathrm{\Gamma }}_o{D}_2^4}$	8a	${\displaystyle (c:a:b):2_1}$${\displaystyle 2_1}$	${\displaystyle (2_1{2}_1\overline{\times })}$
20			C2221	C 2 2 21	${\displaystyle {\mathrm{\Gamma }}_o^b{D}_2^5}$	5a	${\displaystyle \left(\frac{a+b}{2}:c:a:b\right):2_1:2}$	${\displaystyle (2_1\ast 2_1{2}_1)}$	${\displaystyle (2_0{2}_1\ast )}$
21			C222	C 2 2 2	${\displaystyle {\mathrm{\Gamma }}_o^b{D}_2^6}$	10s	${\displaystyle \left(\frac{a+b}{2}:c:a:b\right):2:2}$	${\displaystyle (2_0\ast 2_0{2}_0)}$	${\displaystyle (\ast 2_0{2}_0{2}_1{2}_1)}$
22			F222	F 2 2 2	${\displaystyle {\mathrm{\Gamma }}_o^f{D}_2^7}$	12s	${\displaystyle \left(\frac{a+c}{2}/\frac{b+c}{2}/\frac{a+b}{2}:c:a:b\right):2:2}$	${\displaystyle (\ast 2_0{2}_1{2}_0{2}_1)}$
23			I222	I 2 2 2	${\displaystyle {\mathrm{\Gamma }}_o^v{D}_2^8}$	11s	${\displaystyle \left(\frac{a+b+c}{2}/c:a:b\right):2:2}$	${\displaystyle (2_1\ast 2_0{2}_0)}$
24			I212121	I 21 21 21	${\displaystyle {\mathrm{\Gamma }}_o^v{D}_2^9}$	6a	${\displaystyle \left(\frac{a+b+c}{2}/c:a:b\right):2:2_1}$	${\displaystyle (2_0\ast 2_1{2}_1)}$
25	mm2	${\displaystyle \ast 22}$	Pmm2	P m m 2	${\displaystyle {\mathrm{\Gamma }}_o{C}_{2v}^1}$	13s	${\displaystyle (c:a:b):m\cdot 2}$	${\displaystyle (\ast \cdot 2\cdot 2\cdot 2\cdot 2)}$	${\displaystyle [{\ast }_0\cdot {\ast }_0\cdot ]}$
26			Pmc21	P m c 21	${\displaystyle {\mathrm{\Gamma }}_o{C}_{2v}^2}$	9a	${\displaystyle (c:a:b):\tilde{c}\cdot 2_1}$	${\displaystyle (\ast \cdot 2:2\cdot 2:2)}$	${\displaystyle (\overline{\ast }\cdot \overline{\ast }\cdot )}$,${\displaystyle [{\times }_0{\times }_0]}$
27			Pcc2	P c c 2	${\displaystyle {\mathrm{\Gamma }}_o{C}_{2v}^3}$	5h	${\displaystyle (c:a:b):\tilde{c}\cdot 2}$	${\displaystyle (\ast :2:2:2:2)}$	${\displaystyle ({\overline{\ast }}_0{\overline{\ast }}_0)}$
28			Pma2	P m a 2	${\displaystyle {\mathrm{\Gamma }}_o{C}_{2v}^4}$	6h	${\displaystyle (c:a:b):\tilde{a}\cdot 2}$	${\displaystyle (2_0{2}_0\ast \cdot )}$	${\displaystyle [{\ast }_0:{\ast }_0:]}$,${\displaystyle (\ast \cdot {\ast }_0)}$
29			Pca21	P c a 21	${\displaystyle {\mathrm{\Gamma }}_o{C}_{2v}^5}$	11a	${\displaystyle (c:a:b):\tilde{a}\cdot 2_1}$	${\displaystyle (2_1{2}_1\ast :)}$	${\displaystyle (\overline{\ast }:\overline{\ast }:)}$
30			Pnc2	P n c 2	${\displaystyle {\mathrm{\Gamma }}_o{C}_{2v}^6}$	7h	${\displaystyle (c:a:b):\tilde{c}\odot 2}$	${\displaystyle (2_0{2}_0\ast :)}$	${\displaystyle ({\overline{\ast }}_1{\overline{\ast }}_1)}$,${\displaystyle ({\ast }_0{\times }_0)}$
31			Pmn21	P m n 21	${\displaystyle {\mathrm{\Gamma }}_o{C}_{2v}^7}$	10a	${\displaystyle (c:a:b):\widetilde{ac}\cdot 2_1}$	${\displaystyle (2_1{2}_1\ast \cdot )}$	${\displaystyle (\ast \cdot \overline{\times })}$,${\displaystyle [{\times }_0{\times }_1]}$
32			Pba2	P b a 2	${\displaystyle {\mathrm{\Gamma }}_o{C}_{2v}^8}$	9h	${\displaystyle (c:a:b):\tilde{a}\odot 2}$	${\displaystyle (2_0{2}_0{\times }_0)}$	${\displaystyle (\ast :{\ast }_0)}$
33			Pna21	P n a 21	${\displaystyle {\mathrm{\Gamma }}_o{C}_{2v}^9}$	12a	${\displaystyle (c:a:b):\tilde{a}\odot 2_1}$	${\displaystyle (2_1{2}_1\times )}$	${\displaystyle (\ast :\times )}$,${\displaystyle (\times {\times }_1)}$
34			Pnn2	P n n 2	${\displaystyle {\mathrm{\Gamma }}_o{C}_{2v}^{10}}$	8h	${\displaystyle (c:a:b):\widetilde{ac}\odot 2}$	${\displaystyle (2_0{2}_0{\times }_1)}$	${\displaystyle ({\ast }_0{\times }_1)}$
35			Cmm2	C m m 2	${\displaystyle {\mathrm{\Gamma }}_o^b{C}_{2v}^{11}}$	14s	${\displaystyle \left(\frac{a+b}{2}:c:a:b\right):m\cdot 2}$	${\displaystyle (2_0\ast \cdot 2\cdot 2)}$	${\displaystyle [{\ast }_0\cdot {\ast }_0:]}$
36			Cmc21	C m c 21	${\displaystyle {\mathrm{\Gamma }}_o^b{C}_{2v}^{12}}$	13a	${\displaystyle \left(\frac{a+b}{2}:c:a:b\right):\tilde{c}\cdot 2_1}$	${\displaystyle (2_1\ast \cdot 2:2)}$	${\displaystyle (\overline{\ast }\cdot \overline{\ast }:)}$,${\displaystyle [{\times }_1{\times }_1]}$
37			Ccc2	C c c 2	${\displaystyle {\mathrm{\Gamma }}_o^b{C}_{2v}^{13}}$	10h	${\displaystyle \left(\frac{a+b}{2}:c:a:b\right):\tilde{c}\cdot 2}$	${\displaystyle (2_0\ast :2:2)}$	${\displaystyle ({\overline{\ast }}_0{\overline{\ast }}_1)}$
38			Amm2	A m m 2	${\displaystyle {\mathrm{\Gamma }}_o^b{C}_{2v}^{14}}$	15s	${\displaystyle \left(\frac{b+c}{2}/c:a:b\right):m\cdot 2}$	${\displaystyle (\ast \cdot 2\cdot 2\cdot 2:2)}$	${\displaystyle [{\ast }_1\cdot {\ast }_1\cdot ]}$,${\displaystyle [\ast \cdot {\times }_0]}$
39			Aem2	A b m 2	${\displaystyle {\mathrm{\Gamma }}_o^b{C}_{2v}^{15}}$	11h	${\displaystyle \left(\frac{b+c}{2}/c:a:b\right):m\cdot 2_1}$	${\displaystyle (\ast \cdot 2:2:2:2)}$	${\displaystyle [{\ast }_1:{\ast }_1:]}$,${\displaystyle (\overline{\ast }\cdot {\overline{\ast }}_0)}$
40			Ama2	A m a 2	${\displaystyle {\mathrm{\Gamma }}_o^b{C}_{2v}^{16}}$	12h	${\displaystyle \left(\frac{b+c}{2}/c:a:b\right):\tilde{a}\cdot 2}$	${\displaystyle (2_0{2}_1\ast \cdot )}$	${\displaystyle (\ast \cdot {\ast }_1)}$,${\displaystyle [\ast :{\times }_1]}$
41			Aea2	A b a 2	${\displaystyle {\mathrm{\Gamma }}_o^b{C}_{2v}^{17}}$	13h	${\displaystyle \left(\frac{b+c}{2}/c:a:b\right):\tilde{a}\cdot 2_1}$	${\displaystyle (2_0{2}_1\ast :)}$	${\displaystyle (\ast :{\ast }_1)}$,${\displaystyle (\overline{\ast }:{\overline{\ast }}_1)}$
42			Fmm2	F m m 2	${\displaystyle {\mathrm{\Gamma }}_o^f{C}_{2v}^{18}}$	17s	${\displaystyle \left(\frac{a+c}{2}/\frac{b+c}{2}/\frac{a+b}{2}:c:a:b\right):m\cdot 2}$	${\displaystyle (\ast \cdot 2\cdot 2:2:2)}$	${\displaystyle [{\ast }_1\cdot {\ast }_1:]}$
43			Fdd2	F d d 2	${\displaystyle {\mathrm{\Gamma }}_o^f{C}_{2v}^{19}}$	16h	${\displaystyle \left(\frac{a+c}{2}/\frac{b+c}{2}/\frac{a+b}{2}:c:a:b\right):\frac{1}{2}\widetilde{ac}\odot 2}$	${\displaystyle (2_0{2}_1\times )}$	${\displaystyle ({\ast }_1\times )}$
44			Imm2	I m m 2	${\displaystyle {\mathrm{\Gamma }}_o^v{C}_{2v}^{20}}$	16s	${\displaystyle \left(\frac{a+b+c}{2}/c:a:b\right):m\cdot 2}$	${\displaystyle (2_1\ast \cdot 2\cdot 2)}$	${\displaystyle [\ast \cdot {\times }_1]}$
45			Iba2	I b a 2	${\displaystyle {\mathrm{\Gamma }}_o^v{C}_{2v}^{21}}$	15h	${\displaystyle \left(\frac{a+b+c}{2}/c:a:b\right):\tilde{c}\cdot 2}$	${\displaystyle (2_1\ast :2:2)}$	${\displaystyle (\overline{\ast }:{\overline{\ast }}_0)}$
46			Ima2	I m a 2	${\displaystyle {\mathrm{\Gamma }}_o^v{C}_{2v}^{22}}$	14h	${\displaystyle \left(\frac{a+b+c}{2}/c:a:b\right):\tilde{a}\cdot 2}$	${\displaystyle (2_0\ast \cdot 2:2)}$	${\displaystyle (\overline{\ast }\cdot {\overline{\ast }}_1)}$,${\displaystyle [\ast :{\times }_0]}$
47	${\displaystyle \frac{2}{m}\frac{2}{m}\frac{2}{m}}$	${\displaystyle \ast 222}$	Pmmm	P 2/m 2/m 2/m	${\displaystyle {\mathrm{\Gamma }}_o{D}_{2h}^1}$	18s	${\displaystyle \left(c:a:b\right)\cdot m:2\cdot m}$	${\displaystyle [\ast \cdot 2\cdot 2\cdot 2\cdot 2]}$
48			Pnnn	P 2/n 2/n 2/n	${\displaystyle {\mathrm{\Gamma }}_o{D}_{2h}^2}$	19h	${\displaystyle \left(c:a:b\right)\cdot \widetilde{ab}:2\odot \widetilde{ac}}$	${\displaystyle (2{\overline{\ast }}_1{2}_0{2}_0)}$
49			Pccm	P 2/c 2/c 2/m	${\displaystyle {\mathrm{\Gamma }}_o{D}_{2h}^3}$	17h	${\displaystyle \left(c:a:b\right)\cdot m:2\cdot \tilde{c}}$	${\displaystyle [\ast :2:2:2:2]}$	${\displaystyle (\ast 2_0{2}_{0}2\cdot 2)}$
50			Pban	P 2/b 2/a 2/n	${\displaystyle {\mathrm{\Gamma }}_o{D}_{2h}^4}$	18h	${\displaystyle \left(c:a:b\right)\cdot \widetilde{ab}:2\odot \tilde{a}}$	${\displaystyle (2{\overline{\ast }}_0{2}_0{2}_0)}$	${\displaystyle (\ast 2_0{2}_{0}2:2)}$
51			Pmma	P 21/m 2/m 2/a	${\displaystyle {\mathrm{\Gamma }}_o{D}_{2h}^5}$	14a	${\displaystyle \left(c:a:b\right)\cdot \tilde{a}:2\cdot m}$	${\displaystyle [2_0{2}_0\ast \cdot ]}$	${\displaystyle [\ast \cdot 2:2\cdot 2:2]}$,${\displaystyle [\ast 2\cdot 2\cdot 2\cdot 2]}$
52			Pnna	P 2/n 21/n 2/a	${\displaystyle {\mathrm{\Gamma }}_o{D}_{2h}^6}$	17a	${\displaystyle \left(c:a:b\right)\cdot \tilde{a}:2\odot \widetilde{ac}}$	${\displaystyle (2_{0}2{\overline{\ast }}_1)}$	${\displaystyle (2_0\ast 2:2)}$,${\displaystyle (2\overline{\ast }{2}_1{2}_1)}$
53			Pmna	P 2/m 2/n 21/a	${\displaystyle {\mathrm{\Gamma }}_o{D}_{2h}^7}$	15a	${\displaystyle \left(c:a:b\right)\cdot \tilde{a}:2_1\cdot \widetilde{ac}}$	${\displaystyle [2_0{2}_0\ast :]}$	${\displaystyle (\ast 2_1{2}_{1}2\cdot 2)}$,${\displaystyle (2_0\ast 2\cdot 2)}$
54			Pcca	P 21/c 2/c 2/a	${\displaystyle {\mathrm{\Gamma }}_o{D}_{2h}^8}$	16a	${\displaystyle \left(c:a:b\right)\cdot \tilde{a}:2\cdot \tilde{c}}$	${\displaystyle (2_{0}2{\overline{\ast }}_0)}$	${\displaystyle (\ast 2:2:2:2)}$,${\displaystyle (\ast 2_1{2}_{1}2:2)}$
55			Pbam	P 21/b 21/a 2/m	${\displaystyle {\mathrm{\Gamma }}_o{D}_{2h}^9}$	22a	${\displaystyle \left(c:a:b\right)\cdot m:2\odot \tilde{a}}$	${\displaystyle [2_0{2}_0{\times }_0]}$	${\displaystyle (\ast 2\cdot 2:2\cdot 2)}$
56			Pccn	P 21/c 21/c 2/n	${\displaystyle {\mathrm{\Gamma }}_o{D}_{2h}^{10}}$	27a	${\displaystyle \left(c:a:b\right)\cdot \widetilde{ab}:2\cdot \tilde{c}}$	${\displaystyle (2\overline{\ast }:2:2)}$	${\displaystyle (2_{1}2{\overline{\ast }}_0)}$
57			Pbcm	P 2/b 21/c 21/m	${\displaystyle {\mathrm{\Gamma }}_o{D}_{2h}^{11}}$	23a	${\displaystyle \left(c:a:b\right)\cdot m:2_1\odot \tilde{c}}$	${\displaystyle (2_{0}2\overline{\ast }\cdot )}$	${\displaystyle (\ast 2:2\cdot 2:2)}$,${\displaystyle [2_1{2}_1\ast :]}$
58			Pnnm	P 21/n 21/n 2/m	${\displaystyle {\mathrm{\Gamma }}_o{D}_{2h}^{12}}$	25a	${\displaystyle \left(c:a:b\right)\cdot m:2\odot \widetilde{ac}}$	${\displaystyle [2_0{2}_0{\times }_1]}$	${\displaystyle (2_1\ast 2\cdot 2)}$
59			Pmmn	P 21/m 21/m 2/n	${\displaystyle {\mathrm{\Gamma }}_o{D}_{2h}^{13}}$	24a	${\displaystyle \left(c:a:b\right)\cdot \widetilde{ab}:2\cdot m}$	${\displaystyle (2\overline{\ast }\cdot 2\cdot 2)}$	${\displaystyle [2_1{2}_1\ast \cdot ]}$
60			Pbcn	P 21/b 2/c 21/n	${\displaystyle {\mathrm{\Gamma }}_o{D}_{2h}^{14}}$	26a	${\displaystyle \left(c:a:b\right)\cdot \widetilde{ab}:2_1\odot \tilde{c}}$	${\displaystyle (2_{0}2\overline{\ast }:)}$	${\displaystyle (2_1\ast 2:2)}$,${\displaystyle (2_{1}2{\overline{\ast }}_1)}$
61			Pbca	P 21/b 21/c 21/a	${\displaystyle {\mathrm{\Gamma }}_o{D}_{2h}^{15}}$	29a	${\displaystyle \left(c:a:b\right)\cdot \tilde{a}:2_1\odot \tilde{c}}$	${\displaystyle (2_{1}2\overline{\ast }:)}$
62			Pnma	P 21/n 21/m 21/a	${\displaystyle {\mathrm{\Gamma }}_o{D}_{2h}^{16}}$	28a	${\displaystyle \left(c:a:b\right)\cdot \tilde{a}:2_1\odot m}$	${\displaystyle (2_{1}2\overline{\ast }\cdot )}$	${\displaystyle (2\overline{\ast }\cdot 2:2)}$,${\displaystyle [2_1{2}_1\times ]}$
63			Cmcm	C 2/m 2/c 21/m	${\displaystyle {\mathrm{\Gamma }}_o^b{D}_{2h}^{17}}$	18a	${\displaystyle \left(\frac{a+b}{2}:c:a:b\right)\cdot m:2_1\cdot \tilde{c}}$	${\displaystyle [2_0{2}_1\ast \cdot ]}$	${\displaystyle (\ast 2\cdot 2\cdot 2:2)}$,${\displaystyle [2_1\ast \cdot 2:2]}$
64			Cmce	C 2/m 2/c 21/a	${\displaystyle {\mathrm{\Gamma }}_o^b{D}_{2h}^{18}}$	19a	${\displaystyle \left(\frac{a+b}{2}:c:a:b\right)\cdot \tilde{a}:2_1\cdot \tilde{c}}$	${\displaystyle [2_0{2}_1\ast :]}$	${\displaystyle (\ast 2\cdot 2:2:2)}$,${\displaystyle (\ast 2_{1}2\cdot 2:2)}$
65			Cmmm	C 2/m 2/m 2/m	${\displaystyle {\mathrm{\Gamma }}_o^b{D}_{2h}^{19}}$	19s	${\displaystyle \left(\frac{a+b}{2}:c:a:b\right)\cdot m:2\cdot m}$	${\displaystyle [2_0\ast \cdot 2\cdot 2]}$	${\displaystyle [\ast \cdot 2\cdot 2\cdot 2:2]}$
66			Cccm	C 2/c 2/c 2/m	${\displaystyle {\mathrm{\Gamma }}_o^b{D}_{2h}^{20}}$	20h	${\displaystyle \left(\frac{a+b}{2}:c:a:b\right)\cdot m:2\cdot \tilde{c}}$	${\displaystyle [2_0\ast :2:2]}$	${\displaystyle (\ast 2_0{2}_{1}2\cdot 2)}$
67			Cmme	C 2/m 2/m 2/e	${\displaystyle {\mathrm{\Gamma }}_o^b{D}_{2h}^{21}}$	21h	${\displaystyle \left(\frac{a+b}{2}:c:a:b\right)\cdot \tilde{a}:2\cdot m}$	${\displaystyle (\ast 2_{0}2\cdot 2\cdot 2)}$	${\displaystyle [\ast \cdot 2:2:2:2]}$
68			Ccce	C 2/c 2/c 2/e	${\displaystyle {\mathrm{\Gamma }}_o^b{D}_{2h}^{22}}$	22h	${\displaystyle \left(\frac{a+b}{2}:c:a:b\right)\cdot \tilde{a}:2\cdot \tilde{c}}$	${\displaystyle (\ast 2_{0}2:2:2)}$	${\displaystyle (\ast 2_0{2}_{1}2:2)}$
69			Fmmm	F 2/m 2/m 2/m	${\displaystyle {\mathrm{\Gamma }}_o^f{D}_{2h}^{23}}$	21s	${\displaystyle \left(\frac{a+c}{2}/\frac{b+c}{2}/\frac{a+b}{2}:c:a:b\right)\cdot m:2\cdot m}$	${\displaystyle [\ast \cdot 2\cdot 2:2:2]}$
70			Fddd	F 2/d 2/d 2/d	${\displaystyle {\mathrm{\Gamma }}_o^f{D}_{2h}^{24}}$	24h	${\displaystyle \left(\frac{a+c}{2}/\frac{b+c}{2}/\frac{a+b}{2}:c:a:b\right)\cdot \frac{1}{2}\widetilde{ab}:2\odot \frac{1}{2}\widetilde{ac}}$	${\displaystyle (2\overline{\ast }{2}_0{2}_1)}$
71			Immm	I 2/m 2/m 2/m	${\displaystyle {\mathrm{\Gamma }}_o^v{D}_{2h}^{25}}$	20s	${\displaystyle \left(\frac{a+b+c}{2}/c:a:b\right)\cdot m:2\cdot m}$	${\displaystyle [2_1\ast \cdot 2\cdot 2]}$
72			Ibam	I 2/b 2/a 2/m	${\displaystyle {\mathrm{\Gamma }}_o^v{D}_{2h}^{26}}$	23h	${\displaystyle \left(\frac{a+b+c}{2}/c:a:b\right)\cdot m:2\cdot \tilde{c}}$	${\displaystyle [2_1\ast :2:2]}$	${\displaystyle (\ast 2_{0}2\cdot 2:2)}$
73			Ibca	I 2/b 2/c 2/a	${\displaystyle {\mathrm{\Gamma }}_o^v{D}_{2h}^{27}}$	21a	${\displaystyle \left(\frac{a+b+c}{2}/c:a:b\right)\cdot \tilde{a}:2\cdot \tilde{c}}$	${\displaystyle (\ast 2_{1}2:2:2)}$
74			Imma	I 2/m 2/m 2/a	${\displaystyle {\mathrm{\Gamma }}_o^v{D}_{2h}^{28}}$	20a	${\displaystyle \left(\frac{a+b+c}{2}/c:a:b\right)\cdot \tilde{a}:2\cdot m}$	${\displaystyle (\ast 2_{1}2\cdot 2\cdot 2)}$	${\displaystyle [2_0\ast \cdot 2:2]}$