Subgroups — C₂×C₇×Dic₇ #87646

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
2	C₇×Dic₇	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₇²	C₄	1	2	yes	complemented
4	C₂×C₇²	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₇	—	7	1	no	maximal
6	C₂×Dic₇	C₇	1	1	yes	maximal, characteristic, direct product factor
7	C₇²	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
8	C₂²×C₇	—	2	3	no	—
9	C₂²×C₇	D₇	1	1	yes	characteristic
10	C₂²×C₇	C₂×C₇	1	1	yes	characteristic
11	C₄×C₇	—	7	2	no	—
12	Dic₇	C₂×C₇	1	2	yes	direct product factor
13	C₂×C₇	—	2	6	no	—
14	C₂×C₇	—	2	3	no	—
15	C₂×C₇	Dic₇	1	2	yes	direct product factor
16	C₂×C₇	C₄×C₇	1	2	yes	complemented
17	C₂×C₇	C₂×D₇	1	1	yes	characteristic
18	C₂×C₇	C₂²×C₇	1	1	yes	characteristic
19	C₂×C₄	—	7	1	no	Sylow
20	C₇	—	2	3	no	—
21	C₇	C₂×Dic₇	1	1	yes	characteristic, direct product factor
22	C₇	C₂×C₄×C₇	1	1	yes	characteristic, complemented
23	C₂²	C₇×D₇	1	1	yes	characteristic
24	C₄	—	7	2	no	—
25	C₂	C₇×Dic₇	1	2	yes	direct product factor
26	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.