The correspondence between different notations

Crystal system	Hermann-Mauguin		Shubnikov^[1]	Schoenflies	Orbifold	Coxeter	Order
Crystal system	(full)	(short)	Shubnikov^[1]	Schoenflies	Orbifold	Coxeter	Order
Triclinic	1	1	$1\$	C₁	11	[ ]⁺	1
Triclinic	1	1	$\tilde{2}$	C_i = S₂	×	[2⁺,2⁺]	2
Monoclinic	2	2	$2\$	C₂	22	[2]⁺	2
	m	m	$m\$	C_s = C_1h	*	[ ]	2
	$\tfrac{2}{m}$	2/m	$2:m\$	C_2h	2*	[2,2⁺]	4
Orthorhombic	222	222	$2:2\$	D₂ = V	222	[2,2]⁺	4
	mm2	mm2	$2 \cdot m\$	C_2v	*22	[2]	4
	$\tfrac{2}{m}\tfrac{2}{m}\tfrac{2}{m}$	mmm	$m \cdot 2:m\$	D_2h = V_h	*222	[2,2]	8
Tetragonal	4	4	$4\$	C₄	44	[4]⁺	4
	4	4	$\tilde{4}$	S₄	2×	[2⁺,4⁺]	4
	$\tfrac{4}{m}$	4/m	$4:m\$	C_4h	4*	[2,4⁺]	8
	422	422	$4:2\$	D₄	422	[4,2]⁺	8
	4mm	4mm	$4 \cdot m\$	C_4v	*44	[4]	8
	42m	42m	$\tilde{4}\cdot m$	D_2d = V_d	2*2	[2⁺,4]	8
	$\tfrac{4}{m}\tfrac{2}{m}\tfrac{2}{m}$	4/mmm	$m \cdot 4:m\$	D_4h	*422	[4,2]	16
Trigonal	3	3	$3\$	C₃	33	[3]⁺	3
	3	3	$\tilde{6}$	C_3i = S₆	3×	[2⁺,6⁺]	6
	32	32	$3:2\$	D₃	322	[3,2]⁺	6
	3m	3m	$3 \cdot m\$	C_3v	*33	[3]	6
	3 $\tfrac{2}{m}$	3m	$\tilde{6}\cdot m$	D_3d	2*3	[2⁺,6]	12
Hexagonal	6	6	$6\$	C₆	66	[6]⁺	6
	6	6	$3:m\$	C_3h	3*	[2,3⁺]	6
	$\tfrac{6}{m}$	6/m	$6:m\$	C_6h	6*	[2,6⁺]	12
	622	622	$6:2\$	D₆	622	[6,2]⁺	12
	6mm	6mm	$6 \cdot m\$	C_6v	*66	[6]	12
	6m2	6m2	$m \cdot 3:m\$	D_3h	*322	[3,2]	12
	$\tfrac{6}{m}\tfrac{2}{m}\tfrac{2}{m}$	6/mmm	$m \cdot 6:m\$	D_6h	*622	[6,2]	24
Cubic	23	23	$3/2\$	T	332	[3,3]⁺	12
	$\tfrac{2}{m}$ 3	m3	$\tilde{6}/2$	T_h	3*2	[3⁺,4]	24
	432	432	$3/4\$	O	432	[4,3]⁺	24
	43m	43m	$3/\tilde{4}$	T_d	*332	[3,3]	24
	$\tfrac{4}{m}$ 3 $\tfrac{2}{m}$	m3m	$\tilde{6}/4$	O_h	*432	[4,3]	48