Subgroups — #89317

Order 448.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×Q₃₂	C₂	1	1	yes	maximal, characteristic
2	Dic₅₆	C₂	1	1	yes	maximal, characteristic
3	C₇⋊C₃₂	C₂	1	1	yes	maximal, characteristic
4	C₇×Q₁₆	—	2	1	no	—
5	Dic₂₈	—	2	1	no	—
6	C₇×C₁₆	C₂²	1	1	yes	characteristic
7	Q₆₄	—	7	1	no	maximal, Sylow
8	C₇×Q₈	—	4	1	no	—
9	Dic₁₄	—	4	1	no	—
10	C₇×C₈	D₄	1	1	yes	characteristic
11	Q₃₂	—	7	1	no	—
12	Q₃₂	D₇	1	1	yes	characteristic
13	C₃₂	—	7	1	no	—
14	C₄×C₇	—	8	1	no	—
15	C₄×C₇	D₈	1	1	yes	characteristic
16	Dic₇	—	8	1	no	—
17	Q₁₆	—	2	1	no	—
18	Q₁₆	—	14	1	no	—
19	C₁₆	C₂×D₇	1	1	yes	characteristic
20	C₂×C₇	D₁₆	1	1	yes	characteristic
21	Q₈	—	4	1	no	—
22	Q₈	—	28	1	no	—
23	C₈	C₂²⋊D₇	1	1	yes	characteristic
24	C₇	Q₆₄	1	1	yes	characteristic, complemented, Sylow
25	C₄	—	8	1	no	—
26	C₄	—	56	1	no	—
27	C₄	#1141	1	1	yes	characteristic
28	C₂	#6400	1	1	yes	characteristic

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

N	H ≅ G/N	type
24. C₇	Q₆₄	semidirect

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