Subgroups — C₇⋊#95 #6405

Order 224.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₇	C₂	1	2	yes	maximal
3	C₂³×C₇	C₂²	1	1	yes	characteristic
4	C₂×C₄×C₇	—	2	2	no	—
5	C₂×C₄×C₇	C₄	1	2	yes	complemented
6	C₂×Dic₇	—	2	2	no	—
7	C₂×Dic₇	—	2	2	no	—
8	C₂×Dic₇	C₄	1	4	yes	complemented
9	#95	—	7	1	no	maximal, Sylow
10	C₂²×C₇	C₂×C₄	1	2	yes	—
11	C₂²×C₇	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₇	D₄	1	1	yes	characteristic
13	C₂²×C₇	D₄	1	2	yes	—
14	C₂²×C₇	Q₈	1	1	yes	characteristic
15	C₄×C₇	—	2	2	no	—
16	Dic₇	—	2	4	no	—
17	C₂²×C₄	—	7	2	no	—
18	C₂²×C₄	D₇	1	1	yes	characteristic
19	C₂×C₇	C₄²	1	1	yes	characteristic
20	C₂×C₇	C₂²⋊C₄	1	2	yes	—
21	C₂×C₇	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₇	C₄⋊C₄	1	2	yes	—
23	C₂×C₇	C₄⋊C₄	1	1	yes	characteristic
24	C₂³	C₂×D₇	1	1	yes	characteristic
25	C₂×C₄	—	2	2	no	—
26	C₂×C₄	—	7	4	no	—
27	C₂×C₄	—	14	2	no	—
28	C₂×C₄	—	14	2	no	—
29	C₂×C₄	Dic₇	1	2	yes	complemented
30	C₇	#95	1	1	yes	characteristic, complemented, Sylow
31	C₂²	Dic₁₄	1	1	yes	characteristic
32	C₂²	C₄×D₇	1	2	yes	—
33	C₂²	D₂₈	1	1	yes	characteristic
34	C₂²	C₂×Dic₇	1	1	yes	characteristic
35	C₂²	C₂²⋊D₇	1	2	yes	—
36	C₄	—	2	2	no	—
37	C₄	—	14	4	no	—
38	C₂	C₄×Dic₇	1	1	yes	characteristic
39	C₂	Dic₇⋊C₄	1	2	yes	—
40	C₂	C₄⋊Dic₇	1	1	yes	characteristic
41	C₂	(C₂×D₇)⋊C₄	1	2	yes	—
42	C₂	C₂²⋊Dic₇	1	1	yes	characteristic

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

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