Subgroups — #6489

Order 224.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₇	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊Dic₇	C₂	1	2	yes	maximal
3	C₄⋊Dic₇	C₂	1	2	yes	maximal, complemented
4	C₄×Dic₇	C₂	1	2	yes	maximal, complemented
5	C₂³×C₇	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₇	C₄	1	4	yes	complemented
7	C₂×C₄×C₇	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₇	C₂²	1	1	yes	characteristic
9	C₂×Dic₇	C₂²	1	4	yes	—
10	#117	—	7	1	no	maximal, Sylow
11	C₂²×C₇	—	2	2	no	—
12	C₂²×C₇	C₂×C₄	1	2	yes	—
13	C₂²×C₇	C₂³	1	1	yes	characteristic
14	C₄×C₇	C₂×C₄	1	2	yes	—
15	C₄×C₇	C₂×C₄	1	2	yes	—
16	Dic₇	—	2	4	no	—
17	C₂²×C₄	D₇	1	1	yes	characteristic
18	C₄⋊C₄	—	7	2	no	—
19	C₂²⋊C₄	—	7	2	no	—
20	C₄²	—	7	2	no	—
21	C₂×C₇	—	2	2	no	—
22	C₂×C₇	C₂²×C₄	1	1	yes	characteristic
23	C₂×C₇	#41	1	2	yes	—
24	C₂³	C₂×D₇	1	1	yes	characteristic
25	C₂×C₄	—	7	4	no	—
26	C₂×C₄	Dic₇	1	4	yes	complemented
27	C₂×C₄	C₂×D₇	1	1	yes	characteristic
28	C₂×C₄	C₂×D₇	1	1	yes	characteristic
29	C₇	#117	1	1	yes	characteristic, complemented, Sylow
30	C₂²	—	2	2	no	—
31	C₂²	C₂×Dic₇	1	2	yes	—
32	C₂²	C₂²×D₇	1	1	yes	characteristic
33	C₄	—	14	4	no	—
34	C₄	C₂×Dic₇	1	2	yes	—
35	C₄	C₂×Dic₇	1	2	yes	—
36	C₂	—	2	2	no	—
37	C₂	#1157	1	2	yes	—
38	C₂	C₂²×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.