Subgroups — Q₈×D₇ #1160

Order 112.

38 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, complemented
2	C₄×D₇	C₂	1	3	yes	maximal
3	Dic₁₄	C₂	1	3	yes	maximal, complemented
4	C₂×D₇	C₂²	1	1	yes	characteristic
5	C₄×C₇	C₂²	1	3	yes	—
6	Dic₇	C₂²	1	3	yes	—
7	C₂×Q₈	—	7	1	no	maximal, Sylow
8	C₂×C₇	C₂³	1	1	yes	characteristic
9	D₇	Q₈	1	2	yes	direct product factor
10	Q₈	—	7	3	no	—
11	Q₈	D₇	1	1	yes	characteristic, direct product factor
12	C₂×C₄	—	7	3	no	—
13	C₇	C₂×Q₈	1	1	yes	characteristic, complemented, Sylow
14	C₂²	—	7	1	no	—
15	C₄	—	7	3	no	—
16	C₄	C₂×D₇	1	3	yes	—
17	C₂	—	7	2	no	—
18	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.