Subgroups — Dic₁₁₂ #89245

Order 448.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₅₆	C₂	1	2	yes	maximal
2	C₇×C₃₂	C₂	1	1	yes	maximal, characteristic
3	Dic₂₈	—	2	2	no	—
4	C₇×C₁₆	C₂²	1	1	yes	characteristic
5	Q₆₄	—	7	1	no	maximal, Sylow
6	Dic₁₄	—	4	2	no	—
7	C₇×C₈	D₄	1	1	yes	characteristic
8	Q₃₂	—	7	2	no	—
9	C₃₂	D₇	1	1	yes	characteristic
10	C₄×C₇	D₈	1	1	yes	characteristic
11	Dic₇	—	8	2	no	—
12	Q₁₆	—	14	2	no	—
13	C₁₆	C₂×D₇	1	1	yes	characteristic
14	C₂×C₇	D₁₆	1	1	yes	characteristic
15	Q₈	—	28	2	no	—
16	C₈	D₂₈	1	1	yes	characteristic
17	C₇	Q₆₄	1	1	yes	characteristic, complemented, Sylow
18	C₄	—	56	2	no	—
19	C₄	D₅₆	1	1	yes	characteristic
20	C₂	D₁₁₂	1	1	yes	characteristic

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

N	H ≅ G/N	type
17. C₇	Q₆₄	semidirect

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