Subgroups — Dic₆₀₈₈ #37566847

Order 24352.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₃₀₄₄	C₂	1	2	yes	maximal
2	C₁₆×C₇₆₁	C₂	1	1	yes	maximal, characteristic
3	Dic₁₅₂₂	—	2	2	no	—
4	C₈×C₇₆₁	C₂²	1	1	yes	characteristic
5	C₄×C₇₆₁	D₄	1	1	yes	characteristic
6	Dic₇₆₁	—	4	2	no	—
7	C₂×C₇₆₁	D₈	1	1	yes	characteristic
8	C₇₆₁	Q₃₂	1	1	yes	characteristic, complemented, Sylow
9	Q₃₂	—	761	1	no	maximal, Sylow
10	Q₁₆	—	761	2	no	—
11	C₁₆	D₇₆₁	1	1	yes	characteristic
12	Q₈	—	1522	2	no	—
13	C₈	C₂×D₇₆₁	1	1	yes	characteristic
14	C₄	—	3044	2	no	—
15	C₄	D₃₀₄₄	1	1	yes	characteristic
16	C₂	D₆₀₈₈	1	1	yes	characteristic

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

N	H ≅ G/N	type
8. C₇₆₁	Q₃₂	semidirect

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