Subgroups — #6379

Order 224.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1157	C₂	1	1	yes	maximal, characteristic
2	C₄²×C₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#1136	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×C₇	—	2	1	no	—
5	C₂×C₄×C₇	C₂²	1	1	yes	characteristic
6	C₂²⋊D₇	—	2	1	no	—
7	D₂₈	C₄	1	1	yes	characteristic, complemented
8	C₄×D₇	—	2	1	no	—
9	Dic₁₄	C₄	1	1	yes	characteristic, complemented
10	C₇⋊C₈	—	2	1	no	—
11	#104	—	7	1	no	maximal, Sylow
12	C₂²×C₇	D₄	1	1	yes	characteristic
13	C₂×D₇	—	2	1	no	—
14	C₄×C₇	—	2	2	no	—
15	C₄×C₇	C₂×C₄	1	1	yes	characteristic
16	C₄×C₇	D₄	1	1	yes	characteristic
17	Dic₇	—	2	1	no	—
18	#41	—	7	1	no	—
19	M₁₆	—	7	1	no	—
20	C₄²	D₇	1	1	yes	characteristic, complemented
21	C₂×C₇	—	2	1	no	—
22	C₂×C₇	C₂²⋊C₄	1	1	yes	characteristic
23	D₇	—	4	1	no	—
24	Q₈	—	7	1	no	—
25	D₄	—	7	1	no	—
26	D₄	—	14	1	no	—
27	C₂×C₄	—	2	1	no	—
28	C₂×C₄	—	14	1	no	—
29	C₂×C₄	C₂×D₇	1	1	yes	characteristic
30	C₈	—	14	1	no	—
31	C₇	#104	1	1	yes	characteristic, complemented, Sylow
32	C₂²	—	14	1	no	—
33	C₂²	C₂²⋊D₇	1	1	yes	characteristic
34	C₄	—	2	2	no	—
35	C₄	—	14	1	no	—
36	C₄	C₄×D₇	1	1	yes	characteristic
37	C₄	D₂₈	1	1	yes	characteristic
38	C₂	—	2	1	no	—
39	C₂	—	28	1	no	—
40	C₂	(C₂×D₇)⋊C₄	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.