Subgroups — C₇×M₃₂ #6427

Order 224.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₈	C₂	1	1	yes	maximal, characteristic
2	C₇×C₁₆	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×C₇	C₄	1	1	yes	characteristic
4	C₇×C₈	C₄	1	1	yes	characteristic
5	C₇×C₈	C₂²	1	1	yes	characteristic
6	M₃₂	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂²×C₇	C₈	1	1	yes	characteristic
8	C₄×C₇	C₈	1	1	yes	characteristic
9	C₄×C₇	C₂×C₄	1	1	yes	characteristic
10	C₂×C₈	C₂×C₇	1	1	yes	characteristic
11	C₁₆	C₂×C₇	1	2	yes	complemented
12	C₂×C₇	—	2	1	no	—
13	C₂×C₇	C₂×C₈	1	1	yes	characteristic
14	C₂×C₄	C₄×C₇	1	1	yes	characteristic
15	C₈	C₄×C₇	1	1	yes	characteristic
16	C₈	C₂²×C₇	1	1	yes	characteristic
17	C₇	M₃₂	1	1	yes	characteristic, direct product factor, Sylow
18	C₂²	C₇×C₈	1	1	yes	characteristic
19	C₄	C₇×C₈	1	1	yes	characteristic
20	C₄	C₂×C₄×C₇	1	1	yes	characteristic
21	C₂	—	2	1	no	—
22	C₂	C₂×C₇×C₈	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.