Subgroups — #6410

Order 224.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×Q₈	C₂	1	1	yes	maximal, characteristic
2	#1136	C₂	1	2	yes	maximal
3	C₇×Q₈	—	2	2	no	—
4	C₂×C₄×C₇	C₄	1	2	yes	—
5	C₂×C₄×C₇	C₂²	1	1	yes	characteristic
6	C₇⋊C₈	—	2	2	no	—
7	#101	—	7	1	no	maximal, Sylow
8	C₂²×C₇	C₂×C₄	1	1	yes	characteristic
9	C₄×C₇	—	2	2	no	—
10	C₄×C₇	D₄	1	2	yes	—
11	C₂×Q₈	D₇	1	1	yes	characteristic
12	M₁₆	—	7	2	no	—
13	C₂×C₇	—	2	1	no	—
14	C₂×C₇	C₂²⋊C₄	1	1	yes	characteristic
15	Q₈	—	2	2	no	—
16	C₂×C₄	Dic₇	1	2	yes	—
17	C₂×C₄	C₂×D₇	1	1	yes	characteristic
18	C₈	—	14	2	no	—
19	C₇	#101	1	1	yes	characteristic, complemented, Sylow
20	C₂²	C₂×Dic₇	1	1	yes	characteristic
21	C₄	—	2	2	no	—
22	C₄	C₂²⋊D₇	1	2	yes	—
23	C₂	—	2	1	no	—
24	C₂	C₂²⋊Dic₇	1	1	yes	characteristic

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

N	H ≅ G/N	type
19. C₇	#101	semidirect

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