Subgroups — #6511

Order 224.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#41	C₂	1	1	yes	maximal, characteristic
2	#1136	C₂	1	3	yes	maximal, complemented
3	C₂×C₇⋊C₈	C₂	1	3	yes	maximal, complemented
4	C₇×Q₈	C₄	1	1	yes	characteristic
5	C₇×D₄	C₄	1	3	yes	—
6	C₂×C₄×C₇	C₂²	1	3	yes	—
7	C₇⋊C₈	C₂²	1	1	yes	characteristic
8	C₇⋊C₈	C₂²	1	3	yes	—
9	#131	—	7	1	no	maximal, Sylow
10	C₂²×C₇	C₂×C₄	1	3	yes	—
11	C₄×C₇	C₂×C₄	1	3	yes	—
12	C₄×C₇	C₂³	1	1	yes	characteristic
13	#41	D₇	1	1	yes	characteristic
14	M₁₆	—	7	3	no	—
15	C₂×C₈	—	7	3	no	—
16	C₂×C₇	—	2	3	no	—
17	C₂×C₇	C₂²×C₄	1	1	yes	characteristic
18	Q₈	Dic₇	1	1	yes	characteristic
19	D₄	Dic₇	1	3	yes	—
20	C₂×C₄	C₂×D₇	1	3	yes	—
21	C₈	—	7	1	no	—
22	C₈	—	7	3	no	—
23	C₇	#131	1	1	yes	characteristic, complemented, Sylow
24	C₂²	C₂×Dic₇	1	3	yes	—
25	C₄	C₂×Dic₇	1	3	yes	—
26	C₄	C₂²×D₇	1	1	yes	characteristic
27	C₂	—	2	3	no	—
28	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.