Subgroups — Dic₁₇₉₂ #72212217

Order 7168.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₈₉₆	C₂	1	2	yes	maximal
2	Q₁₀₂₄	—	7	1	no	maximal, Sylow
3	C₇×C₅₁₂	C₂	1	1	yes	maximal, characteristic
4	Dic₄₄₈	—	2	2	no	—
5	C₇×C₂₅₆	C₂²	1	1	yes	characteristic
6	Dic₂₂₄	—	4	2	no	—
7	C₇×C₁₂₈	D₄	1	1	yes	characteristic
8	Q₅₁₂	—	7	2	no	—
9	C₅₁₂	D₇	1	1	yes	characteristic
10	Dic₁₁₂	—	8	2	no	—
11	C₇×C₆₄	D₈	1	1	yes	characteristic
12	Q₂₅₆	—	14	2	no	—
13	C₂₅₆	C₂×D₇	1	1	yes	characteristic
14	Dic₅₆	—	16	2	no	—
15	C₇×C₃₂	D₁₆	1	1	yes	characteristic
16	Q₁₂₈	—	28	2	no	—
17	C₁₂₈	D₂₈	1	1	yes	characteristic
18	Dic₂₈	—	32	2	no	—
19	C₇×C₁₆	D₃₂	1	1	yes	characteristic
20	Q₆₄	—	56	2	no	—
21	C₆₄	D₅₆	1	1	yes	characteristic
22	Dic₁₄	—	64	2	no	—
23	C₇×C₈	D₆₄	1	1	yes	characteristic
24	Q₃₂	—	112	2	no	—
25	C₃₂	D₁₁₂	1	1	yes	characteristic
26	C₄×C₇	D₁₂₈	1	1	yes	characteristic
27	Dic₇	—	128	2	no	—
28	Q₁₆	—	224	2	no	—
29	C₁₆	D₂₂₄	1	1	yes	characteristic
30	C₂×C₇	D₂₅₆	1	1	yes	characteristic
31	Q₈	—	448	2	no	—
32	C₈	D₄₄₈	1	1	yes	characteristic
33	C₇	Q₁₀₂₄	1	1	yes	characteristic, complemented, Sylow
34	C₄	—	896	2	no	—
35	C₄	D₈₉₆	1	1	yes	characteristic
36	C₂	D₁₇₉₂	1	1	yes	characteristic

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

N	H ≅ G/N	type
33. C₇	Q₁₀₂₄	semidirect

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