Subgroups — Dic₅₆ #6375

Order 224.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₂₈	C₂	1	2	yes	maximal
2	C₇×C₁₆	C₂	1	1	yes	maximal, characteristic
3	Dic₁₄	—	2	2	no	—
4	C₇×C₈	C₂²	1	1	yes	characteristic
5	Q₃₂	—	7	1	no	maximal, Sylow
6	C₄×C₇	D₄	1	1	yes	characteristic
7	Dic₇	—	4	2	no	—
8	Q₁₆	—	7	2	no	—
9	C₁₆	D₇	1	1	yes	characteristic
10	C₂×C₇	D₈	1	1	yes	characteristic
11	Q₈	—	14	2	no	—
12	C₈	C₂×D₇	1	1	yes	characteristic
13	C₇	Q₃₂	1	1	yes	characteristic, complemented, Sylow
14	C₄	—	28	2	no	—
15	C₄	D₂₈	1	1	yes	characteristic
16	C₂	D₅₆	1	1	yes	characteristic

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

N	H ≅ G/N	type
13. C₇	Q₃₂	semidirect

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