Subgroups — C₇×C₂²⋊D₇ #87647

Order 392.

47 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇²	—	2	1	no	—
5	C₂×C₇²	C₂²	1	1	yes	characteristic
6	C₇×D₇	—	2	1	no	—
7	C₇×D₄	—	7	1	no	maximal
8	C₂²⋊D₇	C₇	1	1	yes	maximal, characteristic, direct product factor
9	C₇²	D₄	1	1	yes	characteristic, complemented, Sylow
10	C₂²×C₇	—	2	3	no	—
11	C₂²×C₇	—	7	1	no	—
12	C₂²×C₇	D₇	1	1	yes	characteristic, complemented
13	C₂²×C₇	C₂×C₇	1	1	yes	characteristic, complemented
14	C₂×D₇	C₂×C₇	1	1	yes	characteristic, complemented
15	C₄×C₇	—	7	1	no	—
16	Dic₇	C₂×C₇	1	1	yes	characteristic, complemented
17	C₂×C₇	—	2	6	no	—
18	C₂×C₇	—	2	1	no	—
19	C₂×C₇	—	2	1	no	—
20	C₂×C₇	—	2	3	no	—
21	C₂×C₇	—	14	1	no	—
22	C₂×C₇	C₂×D₇	1	1	yes	characteristic
23	C₂×C₇	C₂²×C₇	1	1	yes	characteristic
24	D₇	—	2	1	no	—
25	D₄	—	7	1	no	Sylow
26	C₇	—	2	3	no	—
27	C₇	C₂²⋊D₇	1	1	yes	characteristic, direct product factor
28	C₇	C₇×D₄	1	1	yes	characteristic, complemented
29	C₂²	—	7	1	no	—
30	C₂²	C₇×D₇	1	1	yes	characteristic, complemented
31	C₄	—	7	1	no	—
32	C₂	—	2	1	no	—
33	C₂	—	14	1	no	—
34	C₂	C₂×C₇×D₇	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.