Subgroups — Dic₃₀₅₆ #27132504

Order 12224.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₅₂₈	C₂	1	2	yes	maximal
2	C₃₂×C₁₉₁	C₂	1	1	yes	maximal, characteristic
3	Dic₇₆₄	—	2	2	no	—
4	C₁₆×C₁₉₁	C₂²	1	1	yes	characteristic
5	Dic₃₈₂	—	4	2	no	—
6	C₈×C₁₉₁	D₄	1	1	yes	characteristic
7	C₄×C₁₉₁	D₈	1	1	yes	characteristic
8	Dic₁₉₁	—	8	2	no	—
9	C₂×C₁₉₁	D₁₆	1	1	yes	characteristic
10	C₁₉₁	Q₆₄	1	1	yes	characteristic, complemented, Sylow
11	Q₆₄	—	191	1	no	maximal, Sylow
12	Q₃₂	—	191	2	no	—
13	C₃₂	D₁₉₁	1	1	yes	characteristic
14	Q₁₆	—	382	2	no	—
15	C₁₆	C₂×D₁₉₁	1	1	yes	characteristic
16	Q₈	—	764	2	no	—
17	C₈	D₇₆₄	1	1	yes	characteristic
18	C₄	—	1528	2	no	—
19	C₄	D₁₅₂₈	1	1	yes	characteristic
20	C₂	D₃₀₅₆	1	1	yes	characteristic

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

N	H ≅ G/N	type
10. C₁₉₁	Q₆₄	semidirect

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