Subgroups — #1144

Order 112.

18 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×Q₈	C₂	1	1	yes	maximal, characteristic
2	Dic₁₄	C₂	1	1	yes	maximal, characteristic
3	C₇⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₄×C₇	—	2	1	no	—
5	C₄×C₇	C₂²	1	1	yes	characteristic
6	Dic₇	—	2	1	no	—
7	Q₁₆	—	7	1	no	maximal, Sylow
8	C₂×C₇	D₄	1	1	yes	characteristic
9	Q₈	—	7	1	no	—
10	Q₈	D₇	1	1	yes	characteristic
11	C₈	—	7	1	no	—
12	C₇	Q₁₆	1	1	yes	characteristic, complemented, Sylow
13	C₄	—	2	1	no	—
14	C₄	—	14	1	no	—
15	C₄	C₂×D₇	1	1	yes	characteristic
16	C₂	C₂²⋊D₇	1	1	yes	characteristic

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

N	H ≅ G/N	type
12. C₇	Q₁₆	semidirect

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