Subgroups — C₇×Dic₁₄ #87643

Order 392.

33 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₇²	C₂	1	1	yes	maximal, characteristic
2	C₇×Dic₇	C₂	1	2	yes	maximal
3	C₂×C₇²	C₂²	1	1	yes	characteristic
4	C₇×Q₈	—	7	1	no	maximal
5	Dic₁₄	C₇	1	1	yes	maximal, characteristic, direct product factor
6	C₇²	Q₈	1	1	yes	characteristic, complemented, Sylow
7	C₄×C₇	—	2	3	no	—
8	C₄×C₇	—	7	2	no	—
9	C₄×C₇	D₇	1	1	yes	characteristic
10	C₄×C₇	C₂×C₇	1	1	yes	characteristic
11	Dic₇	C₂×C₇	1	2	yes	—
12	C₂×C₇	—	2	3	no	—
13	C₂×C₇	C₂×D₇	1	1	yes	characteristic
14	C₂×C₇	C₂²×C₇	1	1	yes	characteristic
15	Q₈	—	7	1	no	Sylow
16	C₇	—	2	3	no	—
17	C₇	Dic₁₄	1	1	yes	characteristic, direct product factor
18	C₇	C₇×Q₈	1	1	yes	characteristic, complemented
19	C₄	—	7	2	no	—
20	C₄	C₇×D₇	1	1	yes	characteristic
21	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.