Subgroups — Dic₁₅₅₂ #20260576

Order 6208.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₇₇₆	C₂	1	2	yes	maximal
2	C₃₂×C₉₇	C₂	1	1	yes	maximal, characteristic
3	Dic₃₈₈	—	2	2	no	—
4	C₁₆×C₉₇	C₂²	1	1	yes	characteristic
5	Dic₁₉₄	—	4	2	no	—
6	C₈×C₉₇	D₄	1	1	yes	characteristic
7	C₄×C₉₇	D₈	1	1	yes	characteristic
8	Dic₉₇	—	8	2	no	—
9	C₂×C₉₇	D₁₆	1	1	yes	characteristic
10	C₉₇	Q₆₄	1	1	yes	characteristic, complemented, Sylow
11	Q₆₄	—	97	1	no	maximal, Sylow
12	Q₃₂	—	97	2	no	—
13	C₃₂	D₉₇	1	1	yes	characteristic
14	Q₁₆	—	194	2	no	—
15	C₁₆	C₂×D₉₇	1	1	yes	characteristic
16	Q₈	—	388	2	no	—
17	C₈	D₃₈₈	1	1	yes	characteristic
18	C₄	—	776	2	no	—
19	C₄	D₇₇₆	1	1	yes	characteristic
20	C₂	D₁₅₅₂	1	1	yes	characteristic

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

N	H ≅ G/N	type
10. C₉₇	Q₆₄	semidirect