Subgroups — Dic₆₇₅₂ #41011616

Order 27008.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₃₃₇₆	C₂	1	2	yes	maximal
2	C₆₄×C₂₁₁	C₂	1	1	yes	maximal, characteristic
3	Dic₁₆₈₈	—	2	2	no	—
4	C₃₂×C₂₁₁	C₂²	1	1	yes	characteristic
5	Dic₈₄₄	—	4	2	no	—
6	C₁₆×C₂₁₁	D₄	1	1	yes	characteristic
7	Dic₄₂₂	—	8	2	no	—
8	C₈×C₂₁₁	D₈	1	1	yes	characteristic
9	C₄×C₂₁₁	D₁₆	1	1	yes	characteristic
10	Dic₂₁₁	—	16	2	no	—
11	C₂×C₂₁₁	D₃₂	1	1	yes	characteristic
12	C₂₁₁	Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
13	Q₁₂₈	—	211	1	no	maximal, Sylow
14	Q₆₄	—	211	2	no	—
15	C₆₄	D₂₁₁	1	1	yes	characteristic
16	Q₃₂	—	422	2	no	—
17	C₃₂	C₂×D₂₁₁	1	1	yes	characteristic
18	Q₁₆	—	844	2	no	—
19	C₁₆	D₈₄₄	1	1	yes	characteristic
20	Q₈	—	1688	2	no	—
21	C₈	D₁₆₈₈	1	1	yes	characteristic
22	C₄	—	3376	2	no	—
23	C₄	D₃₃₇₆	1	1	yes	characteristic
24	C₂	D₆₇₅₂	1	1	yes	characteristic

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

N	H ≅ G/N	type
12. C₂₁₁	Q₁₂₈	semidirect

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