Subgroups — #6374

Order 224.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₂₈	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅₆	C₂	1	1	yes	maximal, characteristic
3	C₇×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	D₂₈	—	2	1	no	—
5	Dic₁₄	—	2	1	no	—
6	C₇×C₈	C₂²	1	1	yes	characteristic
7	SD₃₂	—	7	1	no	maximal, Sylow
8	C₂×D₇	—	4	1	no	—
9	C₄×C₇	D₄	1	1	yes	characteristic
10	Dic₇	—	4	1	no	—
11	Q₁₆	—	7	1	no	—
12	D₈	—	7	1	no	—
13	C₁₆	D₇	1	1	yes	characteristic, complemented
14	C₂×C₇	D₈	1	1	yes	characteristic
15	D₇	—	8	1	no	—
16	Q₈	—	14	1	no	—
17	D₄	—	14	1	no	—
18	C₈	C₂×D₇	1	1	yes	characteristic
19	C₇	SD₃₂	1	1	yes	characteristic, complemented, Sylow
20	C₂²	—	28	1	no	—
21	C₄	—	28	1	no	—
22	C₄	D₂₈	1	1	yes	characteristic
23	C₂	—	56	1	no	—
24	C₂	D₅₆	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.