Subgroups — Dic₆₀₅₆ #37564334

Order 24224.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₃₀₂₈	C₂	1	2	yes	maximal
2	C₁₆×C₇₅₇	C₂	1	1	yes	maximal, characteristic
3	Dic₁₅₁₄	—	2	2	no	—
4	C₈×C₇₅₇	C₂²	1	1	yes	characteristic
5	C₄×C₇₅₇	D₄	1	1	yes	characteristic
6	Dic₇₅₇	—	4	2	no	—
7	C₂×C₇₅₇	D₈	1	1	yes	characteristic
8	C₇₅₇	Q₃₂	1	1	yes	characteristic, complemented, Sylow
9	Q₃₂	—	757	1	no	maximal, Sylow
10	Q₁₆	—	757	2	no	—
11	C₁₆	D₇₅₇	1	1	yes	characteristic
12	Q₈	—	1514	2	no	—
13	C₈	C₂×D₇₅₇	1	1	yes	characteristic
14	C₄	—	3028	2	no	—
15	C₄	D₃₀₂₈	1	1	yes	characteristic
16	C₂	D₆₀₅₆	1	1	yes	characteristic

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

N	H ≅ G/N	type
8. C₇₅₇	Q₃₂	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.