Subgroups — C₂²⋊(C₇⋊D₇) #87652

Order 392.

80 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	C₂²⋊D₇	—	7	8	no	maximal
8	C₇²	D₄	1	1	yes	characteristic, complemented, Sylow
9	C₂²×C₇	D₇	1	8	yes	complemented
10	C₂×D₇	—	7	8	no	—
11	Dic₇	—	7	8	no	—
12	C₂×C₇	—	2	8	no	—
13	C₂×C₇	C₂×D₇	1	8	yes	—
14	D₇	—	14	8	no	—
15	D₄	—	49	1	no	Sylow
16	C₇	C₂²⋊D₇	1	8	yes	complemented
17	C₂²	—	49	1	no	—
18	C₂²	C₇⋊D₇	1	1	yes	characteristic, complemented
19	C₄	—	49	1	no	—
20	C₂	—	2	1	no	—
21	C₂	—	98	1	no	—
22	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.