Subgroups — #1141

Order 112.

22 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	D₂₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₇	—	2	1	no	—
5	C₂×D₇	—	2	1	no	—
6	C₄×C₇	C₂²	1	1	yes	characteristic
7	D₈	—	7	1	no	maximal, Sylow
8	C₂×C₇	—	4	1	no	—
9	C₂×C₇	D₄	1	1	yes	characteristic
10	D₇	—	4	1	no	—
11	D₄	—	7	1	no	—
12	D₄	D₇	1	1	yes	characteristic, complemented
13	C₈	—	7	1	no	—
14	C₇	D₈	1	1	yes	characteristic, complemented, Sylow
15	C₂²	—	2	1	no	—
16	C₂²	—	14	1	no	—
17	C₄	C₂×D₇	1	1	yes	characteristic
18	C₂	—	4	1	no	—
19	C₂	—	28	1	no	—
20	C₂	C₂²⋊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.