Subgroups — Dic₂₂₇₂ #22586558

Order 9088.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₁₃₆	C₂	1	2	yes	maximal
2	C₆₄×C₇₁	C₂	1	1	yes	maximal, characteristic
3	Dic₅₆₈	—	2	2	no	—
4	C₃₂×C₇₁	C₂²	1	1	yes	characteristic
5	Dic₂₈₄	—	4	2	no	—
6	C₁₆×C₇₁	D₄	1	1	yes	characteristic
7	Dic₁₄₂	—	8	2	no	—
8	C₈×C₇₁	D₈	1	1	yes	characteristic
9	C₄×C₇₁	D₁₆	1	1	yes	characteristic
10	Dic₇₁	—	16	2	no	—
11	C₂×C₇₁	D₃₂	1	1	yes	characteristic
12	Q₁₂₈	—	71	1	no	maximal, Sylow
13	C₇₁	Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
14	Q₆₄	—	71	2	no	—
15	C₆₄	D₇₁	1	1	yes	characteristic
16	Q₃₂	—	142	2	no	—
17	C₃₂	C₂×D₇₁	1	1	yes	characteristic
18	Q₁₆	—	284	2	no	—
19	C₁₆	D₂₈₄	1	1	yes	characteristic
20	Q₈	—	568	2	no	—
21	C₈	D₅₆₈	1	1	yes	characteristic
22	C₄	—	1136	2	no	—
23	C₄	D₁₁₃₆	1	1	yes	characteristic
24	C₂	D₂₂₇₂	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
13. C₇₁	Q₁₂₈	semidirect