Subgroups — Dic₃₅₈₄ #72214643

Order 14336.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₇₉₂	C₂	1	2	yes	maximal
2	Dic₈₉₆	—	2	2	no	—
3	Q₂₀₄₈	—	7	1	no	maximal, Sylow
4	Q₁₀₂₄	—	7	2	no	—
5	C₇×C₁₀₂₄	C₂	1	1	yes	maximal, characteristic
6	C₇×C₅₁₂	C₂²	1	1	yes	characteristic
7	C₁₀₂₄	D₇	1	1	yes	characteristic
8	Dic₄₄₈	—	4	2	no	—
9	C₇×C₂₅₆	D₄	1	1	yes	characteristic
10	Dic₂₂₄	—	8	2	no	—
11	C₇×C₁₂₈	D₈	1	1	yes	characteristic
12	Q₅₁₂	—	14	2	no	—
13	C₅₁₂	C₂×D₇	1	1	yes	characteristic
14	Dic₁₁₂	—	16	2	no	—
15	C₇×C₆₄	D₁₆	1	1	yes	characteristic
16	Q₂₅₆	—	28	2	no	—
17	C₂₅₆	D₂₈	1	1	yes	characteristic
18	Dic₅₆	—	32	2	no	—
19	C₇×C₃₂	D₃₂	1	1	yes	characteristic
20	Q₁₂₈	—	56	2	no	—
21	C₁₂₈	D₅₆	1	1	yes	characteristic
22	Dic₂₈	—	64	2	no	—
23	C₇×C₁₆	D₆₄	1	1	yes	characteristic
24	Q₆₄	—	112	2	no	—
25	C₆₄	D₁₁₂	1	1	yes	characteristic
26	Dic₁₄	—	128	2	no	—
27	C₇×C₈	D₁₂₈	1	1	yes	characteristic
28	Q₃₂	—	224	2	no	—
29	C₃₂	D₂₂₄	1	1	yes	characteristic
30	C₄×C₇	D₂₅₆	1	1	yes	characteristic
31	Dic₇	—	256	2	no	—
32	Q₁₆	—	448	2	no	—
33	C₁₆	D₄₄₈	1	1	yes	characteristic
34	C₂×C₇	D₅₁₂	1	1	yes	characteristic
35	Q₈	—	896	2	no	—
36	C₈	D₈₉₆	1	1	yes	characteristic
37	C₇	Q₂₀₄₈	1	1	yes	characteristic, complemented, Sylow
38	C₄	—	1792	2	no	—
39	C₄	D₁₇₉₂	1	1	yes	characteristic
40	C₂	D₃₅₈₄	1	1	yes	characteristic

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

N	H ≅ G/N	type
37. C₇	Q₂₀₄₈	semidirect

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