Subgroups — #6407

Order 224.

46 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	#1136	C₂	1	2	yes	maximal, complemented
3	C₂³×C₇	C₄	1	2	yes	—
4	C₇×D₄	—	2	2	no	—
5	C₂×C₄×C₇	C₂²	1	1	yes	characteristic
6	C₇⋊C₈	—	2	2	no	—
7	#100	—	7	1	no	maximal, Sylow
8	C₂²×C₇	—	2	2	no	—
9	C₂²×C₇	—	4	2	no	—
10	C₂²×C₇	C₂×C₄	1	1	yes	characteristic
11	C₄×C₇	D₄	1	2	yes	—
12	C₂×D₄	D₇	1	1	yes	characteristic
13	M₁₆	—	7	2	no	—
14	C₂×C₇	—	2	1	no	—
15	C₂×C₇	—	4	2	no	—
16	C₂×C₇	C₂²⋊C₄	1	1	yes	characteristic
17	C₂³	Dic₇	1	2	yes	—
18	D₄	—	2	2	no	—
19	C₂×C₄	C₂×D₇	1	1	yes	characteristic
20	C₈	—	14	2	no	—
21	C₇	#100	1	1	yes	characteristic, complemented, Sylow
22	C₂²	—	2	2	no	—
23	C₂²	—	4	2	no	—
24	C₂²	C₂×Dic₇	1	1	yes	characteristic
25	C₄	C₂²⋊D₇	1	2	yes	—
26	C₂	—	2	1	no	—
27	C₂	—	4	2	no	—
28	C₂	C₂²⋊Dic₇	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. #1136	C₂	semidirect
21. C₇	#100	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.