Subgroups — #6381

Order 224.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Dic₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₇⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₇	—	2	1	no	—
5	C₂×C₄×C₇	C₂²	1	1	yes	characteristic
6	C₂×Dic₇	—	2	1	no	—
7	C₇⋊C₈	C₄	1	2	yes	complemented
8	#107	—	7	1	no	maximal, Sylow
9	C₂²×C₇	D₄	1	1	yes	characteristic
10	C₄×C₇	—	4	1	no	—
11	C₄×C₇	C₂×C₄	1	1	yes	characteristic
12	C₄×C₇	Q₈	1	1	yes	characteristic
13	Dic₇	—	4	1	no	—
14	C₂×C₈	—	7	1	no	—
15	C₄⋊C₄	—	7	1	no	—
16	C₄⋊C₄	D₇	1	1	yes	characteristic
17	C₂×C₇	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₇	D₈	1	1	yes	characteristic
19	C₂×C₇	Q₁₆	1	1	yes	characteristic
20	C₂×C₄	—	2	1	no	—
21	C₂×C₄	—	14	1	no	—
22	C₂×C₄	C₂×D₇	1	1	yes	characteristic
23	C₈	—	7	2	no	—
24	C₇	#107	1	1	yes	characteristic, complemented, Sylow
25	C₂²	C₂²⋊D₇	1	1	yes	characteristic
26	C₄	—	4	1	no	—
27	C₄	—	28	1	no	—
28	C₄	Dic₁₄	1	1	yes	characteristic
29	C₄	C₄×D₇	1	1	yes	characteristic
30	C₂	Dic₇⋊C₄	1	1	yes	characteristic
31	C₂	#1141	1	1	yes	characteristic
32	C₂	#1144	1	1	yes	characteristic

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

N	H ≅ G/N	type
7. C₇⋊C₈	C₄	semidirect
24. C₇	#107	semidirect

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