Subgroups — #1136

Order 112.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₇	C₂	1	1	yes	maximal, characteristic
2	C₇⋊C₈	C₂	1	2	yes	maximal, complemented
3	C₂²×C₇	C₄	1	1	yes	characteristic
4	C₄×C₇	C₄	1	1	yes	characteristic
5	C₄×C₇	C₂²	1	1	yes	characteristic
6	M₁₆	—	7	1	no	maximal, Sylow
7	C₂×C₇	—	2	1	no	—
8	C₂×C₇	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄	D₇	1	1	yes	characteristic
10	C₈	—	7	2	no	—
11	C₇	M₁₆	1	1	yes	characteristic, complemented, Sylow
12	C₂²	Dic₇	1	1	yes	characteristic
13	C₄	Dic₇	1	1	yes	characteristic
14	C₄	C₂×D₇	1	1	yes	characteristic
15	C₂	—	2	1	no	—
16	C₂	C₂×Dic₇	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₇⋊C₈	C₂	semidirect
11. C₇	M₁₆	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.