Subgroups — #6400

Order 224.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₈	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×D₄	—	2	1	no	—
5	D₂₈	—	2	1	no	—
6	C₇×C₈	C₂²	1	1	yes	characteristic
7	D₁₆	—	7	1	no	maximal, Sylow
8	C₂²×C₇	—	4	1	no	—
9	C₂×D₇	—	4	1	no	—
10	C₄×C₇	D₄	1	1	yes	characteristic
11	D₈	—	7	1	no	—
12	D₈	D₇	1	1	yes	characteristic, complemented
13	C₁₆	—	7	1	no	—
14	C₂×C₇	—	8	1	no	—
15	C₂×C₇	D₈	1	1	yes	characteristic
16	D₇	—	8	1	no	—
17	D₄	—	2	1	no	—
18	D₄	—	14	1	no	—
19	C₈	C₂×D₇	1	1	yes	characteristic
20	C₇	D₁₆	1	1	yes	characteristic, complemented, Sylow
21	C₂²	—	4	1	no	—
22	C₂²	—	28	1	no	—
23	C₄	C₂²⋊D₇	1	1	yes	characteristic
24	C₂	—	8	1	no	—
25	C₂	—	56	1	no	—
26	C₂	#1141	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.