Subgroups — C₈×D₇ #1130

Order 112.

22 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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