Subgroups — Dic₅₉₁₂ #37556607

Order 23648.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₂₉₅₆	C₂	1	2	yes	maximal
2	C₁₆×C₇₃₉	C₂	1	1	yes	maximal, characteristic
3	Dic₁₄₇₈	—	2	2	no	—
4	C₈×C₇₃₉	C₂²	1	1	yes	characteristic
5	C₄×C₇₃₉	D₄	1	1	yes	characteristic
6	Dic₇₃₉	—	4	2	no	—
7	C₂×C₇₃₉	D₈	1	1	yes	characteristic
8	C₇₃₉	Q₃₂	1	1	yes	characteristic, complemented, Sylow
9	Q₃₂	—	739	1	no	maximal, Sylow
10	Q₁₆	—	739	2	no	—
11	C₁₆	D₇₃₉	1	1	yes	characteristic
12	Q₈	—	1478	2	no	—
13	C₈	C₂×D₇₃₉	1	1	yes	characteristic
14	C₄	—	2956	2	no	—
15	C₄	D₂₉₅₆	1	1	yes	characteristic
16	C₂	D₅₉₁₂	1	1	yes	characteristic

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

N	H ≅ G/N	type
8. C₇₃₉	Q₃₂	semidirect

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