Subgroups — #6398

Order 224.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₄	C₂	1	1	yes	maximal, characteristic
2	C₇×M₁₆	C₂	1	1	yes	maximal, characteristic
3	#1136	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₇	C₂²	1	1	yes	characteristic
5	C₂×Dic₇	C₄	1	2	yes	—
6	Dic₁₄	—	2	1	no	—
7	Dic₁₄	—	2	1	no	—
8	C₇×C₈	—	2	1	no	—
9	C₇⋊C₈	—	2	1	no	—
10	#101	—	7	1	no	maximal, Sylow
11	C₂²×C₇	C₂×C₄	1	1	yes	characteristic
12	C₄×C₇	D₄	1	1	yes	characteristic
13	C₄×C₇	D₄	1	1	yes	characteristic
14	Dic₇	—	2	2	no	—
15	C₂×Q₈	—	7	1	no	—
16	M₁₆	—	7	1	no	—
17	M₁₆	D₇	1	1	yes	characteristic
18	C₂×C₇	—	2	1	no	—
19	C₂×C₇	C₂²⋊C₄	1	1	yes	characteristic
20	Q₈	—	14	1	no	—
21	Q₈	—	14	1	no	—
22	C₂×C₄	—	7	2	no	—
23	C₂×C₄	C₂×D₇	1	1	yes	characteristic
24	C₈	—	2	1	no	—
25	C₈	—	14	1	no	—
26	C₇	#101	1	1	yes	characteristic, complemented, Sylow
27	C₂²	C₄×D₇	1	1	yes	characteristic
28	C₄	—	14	2	no	—
29	C₄	D₂₈	1	1	yes	characteristic
30	C₄	C₂²⋊D₇	1	1	yes	characteristic
31	C₂	—	2	1	no	—
32	C₂	(C₂×D₇)⋊C₄	1	1	yes	characteristic

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

N	H ≅ G/N	type
26. C₇	#101	semidirect

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