Subgroups — #6408

Order 224.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊Dic₇	C₂	1	2	yes	maximal, complemented
3	C₂³×C₇	C₄	1	1	yes	characteristic, complemented
4	C₂³×C₇	C₂²	1	1	yes	characteristic
5	C₇×D₄	—	2	2	no	—
6	C₂×C₄×C₇	C₄	1	1	yes	characteristic, complemented
7	C₂×Dic₇	—	2	2	no	—
8	#99	—	7	1	no	maximal, Sylow
9	C₂²×C₇	—	2	1	no	—
10	C₂²×C₇	—	4	1	no	—
11	C₂²×C₇	—	4	1	no	—
12	C₂²×C₇	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₇	D₄	1	2	yes	—
14	C₄×C₇	—	2	1	no	—
15	Dic₇	—	4	2	no	—
16	C₂×D₄	D₇	1	1	yes	characteristic
17	C₂²⋊C₄	—	7	2	no	—
18	C₂×C₇	—	2	2	no	—
19	C₂×C₇	—	2	1	no	—
20	C₂×C₇	—	4	1	no	—
21	C₂×C₇	C₂²⋊C₄	1	1	yes	characteristic
22	C₂³	Dic₇	1	1	yes	characteristic, complemented
23	C₂³	C₂×D₇	1	1	yes	characteristic
24	D₄	—	2	2	no	—
25	C₂×C₄	—	14	2	no	—
26	C₂×C₄	Dic₇	1	1	yes	characteristic, complemented
27	C₇	#99	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	2	1	no	—
29	C₂²	—	4	1	no	—
30	C₂²	—	4	1	no	—
31	C₂²	C₂×Dic₇	1	1	yes	characteristic
32	C₂²	C₂²⋊D₇	1	2	yes	—
33	C₄	—	2	1	no	—
34	C₄	—	28	2	no	—
35	C₂	—	2	2	no	—
36	C₂	—	2	1	no	—
37	C₂	—	4	1	no	—
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.