Subgroups — C₇×C₇⋊#90673 #36370607

Order 22148.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×D₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₇²×C₁₁₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇⋊#90673	C₇	1	1	yes	maximal, characteristic, direct product factor
4	C₇×#90673	—	7	1	no	maximal
5	C₇×D₁₁₃	—	2	3	no	—
6	C₇×D₁₁₃	D₇	1	1	yes	characteristic
7	C₇×D₁₁₃	C₂×C₇	1	1	yes	characteristic
8	C₇×C₁₁₃	—	2	3	no	—
9	C₇×C₁₁₃	Dic₇	1	1	yes	characteristic, complemented
10	C₇×C₁₁₃	C₄×C₇	1	1	yes	characteristic, complemented
11	#90673	—	7	1	no	Hall
12	D₁₁₃	C₇×D₇	1	1	yes	characteristic
13	C₇×Dic₇	—	113	1	no	maximal, Hall
14	C₁₁₃	C₇×Dic₇	1	1	yes	characteristic, complemented, Sylow
15	C₂×C₇²	—	113	1	no	—
16	C₇²	#90673	1	1	yes	characteristic, complemented, Sylow
17	C₄×C₇	—	791	1	no	—
18	Dic₇	—	113	1	no	—
19	C₂×C₇	—	113	1	no	—
20	C₂×C₇	—	113	1	no	—
21	C₂×C₇	—	226	3	no	—
22	C₇	—	2	3	no	—
23	C₇	C₇×#90673	1	1	yes	characteristic, complemented
24	C₇	C₇⋊#90673	1	1	yes	characteristic, direct product factor
25	C₄	—	791	1	no	Sylow
26	C₂	—	113	1	no	—

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.