Subgroups — #6516

Order 224.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂²⋊D₇	C₂	1	3	yes	maximal, complemented
3	C₂²⋊Dic₇	C₂	1	3	yes	maximal, complemented
4	C₂³×C₇	—	2	6	no	—
5	C₂³×C₇	C₂²	1	3	yes	—
6	C₂²×D₇	C₂²	1	1	yes	characteristic, complemented
7	C₂²⋊D₇	—	2	6	no	—
8	C₂×Dic₇	C₂²	1	3	yes	complemented
9	#120	—	7	1	no	maximal, Sylow
10	C₂²×C₇	—	2	8	no	—
11	C₂²×C₇	—	2	6	no	—
12	C₂²×C₇	D₄	1	6	yes	complemented
13	C₂²×C₇	C₂³	1	1	yes	characteristic
14	C₂×D₇	—	2	3	no	—
15	Dic₇	—	2	3	no	—
16	C₂⁴	D₇	1	1	yes	characteristic, complemented
17	C₂×D₄	—	7	3	no	—
18	C₂²⋊C₄	—	7	3	no	—
19	C₂×C₇	—	2	6	no	—
20	C₂×C₇	C₂×D₄	1	3	yes	—
21	D₇	—	4	1	no	—
22	C₂³	—	2	6	no	—
23	C₂³	—	7	1	no	—
24	C₂³	C₂×D₇	1	3	yes	—
25	D₄	—	14	6	no	—
26	C₂×C₄	—	7	3	no	—
27	C₇	#120	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	2	8	no	—
29	C₂²	—	2	6	no	—
30	C₂²	—	14	3	no	—
31	C₂²	C₂²⋊D₇	1	6	yes	complemented
32	C₂²	C₂²×D₇	1	1	yes	characteristic
33	C₄	—	14	3	no	—
34	C₂	—	2	6	no	—
35	C₂	—	28	1	no	—
36	C₂	C₂×C₂²⋊D₇	1	3	yes	—

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.