Subgroups — #6372

Order 224.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×D₇	C₂	1	1	yes	maximal, characteristic
2	C₇×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×D₇	C₄	1	1	yes	characteristic
5	C₇×C₈	C₂²	1	1	yes	characteristic
6	C₇⋊C₈	C₄	1	1	yes	characteristic
7	M₃₂	—	7	1	no	maximal, Sylow
8	C₂×D₇	C₈	1	1	yes	characteristic
9	C₄×C₇	C₂×C₄	1	1	yes	characteristic
10	Dic₇	C₈	1	1	yes	characteristic
11	C₂×C₈	—	7	1	no	—
12	C₁₆	—	7	1	no	—
13	C₁₆	D₇	1	1	yes	characteristic, complemented
14	C₂×C₇	C₂×C₈	1	1	yes	characteristic
15	D₇	—	2	1	no	—
16	C₂×C₄	—	7	1	no	—
17	C₈	—	7	1	no	—
18	C₈	C₂×D₇	1	1	yes	characteristic
19	C₇	M₃₂	1	1	yes	characteristic, complemented, Sylow
20	C₂²	—	7	1	no	—
21	C₄	—	7	1	no	—
22	C₄	C₄×D₇	1	1	yes	characteristic
23	C₂	—	14	1	no	—
24	C₂	C₈×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.