Subgroups — C₇×D₂₈ #87645

Order 392.

41 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×D₇	C₂	1	2	yes	maximal, complemented
2	C₄×C₇²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇²	C₂²	1	1	yes	characteristic
4	C₇×D₇	—	2	2	no	—
5	C₇×D₄	—	7	1	no	maximal
6	D₂₈	C₇	1	1	yes	maximal, characteristic, direct product factor
7	C₇²	D₄	1	1	yes	characteristic, complemented, Sylow
8	C₂²×C₇	—	7	2	no	—
9	C₂×D₇	C₂×C₇	1	2	yes	complemented
10	C₄×C₇	—	2	3	no	—
11	C₄×C₇	D₇	1	1	yes	characteristic, complemented
12	C₄×C₇	C₂×C₇	1	1	yes	characteristic, complemented
13	C₂×C₇	—	2	3	no	—
14	C₂×C₇	—	14	2	no	—
15	C₂×C₇	C₂×D₇	1	1	yes	characteristic
16	C₂×C₇	C₂²×C₇	1	1	yes	characteristic
17	D₇	—	2	2	no	—
18	D₄	—	7	1	no	Sylow
19	C₇	—	2	3	no	—
20	C₇	D₂₈	1	1	yes	characteristic, direct product factor
21	C₇	C₇×D₄	1	1	yes	characteristic, complemented
22	C₂²	—	7	2	no	—
23	C₄	C₇×D₇	1	1	yes	characteristic, complemented
24	C₂	—	14	2	no	—
25	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.