Subgroups — #6392

Order 224.

36 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	C₄⋊Dic₇	C₂	1	2	yes	maximal
3	C₂×C₄×C₇	C₂²	1	1	yes	characteristic
4	C₂×Dic₇	—	2	2	no	—
5	C₇×C₈	C₄	1	2	yes	complemented
6	#107	—	7	1	no	maximal, Sylow
7	C₂²×C₇	D₄	1	1	yes	characteristic
8	C₄×C₇	C₂×C₄	1	1	yes	characteristic
9	C₄×C₇	Q₈	1	1	yes	characteristic
10	Dic₇	—	4	2	no	—
11	C₂×C₈	D₇	1	1	yes	characteristic
12	C₄⋊C₄	—	7	2	no	—
13	C₂×C₇	C₄⋊C₄	1	1	yes	characteristic
14	C₂×C₇	D₈	1	1	yes	characteristic
15	C₂×C₇	Q₁₆	1	1	yes	characteristic
16	C₂×C₄	—	14	2	no	—
17	C₂×C₄	C₂×D₇	1	1	yes	characteristic
18	C₈	Dic₇	1	2	yes	complemented
19	C₇	#107	1	1	yes	characteristic, complemented, Sylow
20	C₂²	D₂₈	1	1	yes	characteristic
21	C₄	—	28	2	no	—
22	C₄	Dic₁₄	1	1	yes	characteristic
23	C₄	C₂×Dic₇	1	1	yes	characteristic
24	C₂	D₅₆	1	1	yes	characteristic
25	C₂	Dic₂₈	1	1	yes	characteristic
26	C₂	C₄⋊Dic₇	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.