Subgroups — C₇×#16813357 #38759790

Order 25228.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₉₀₁	C₂	1	1	yes	maximal, characteristic
2	C₇×C₁₇×C₅₃	C₄	1	1	yes	characteristic, complemented, Hall
3	#16813357	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	D₉₀₁	C₂×C₇	1	1	yes	characteristic
5	C₇×#6157	—	17	1	no	maximal, Hall
6	C₁₇×C₅₃	C₄×C₇	1	1	yes	characteristic, complemented, Hall
7	C₇×D₅₃	—	17	1	no	—
8	C₇×#595	—	53	1	no	maximal, Hall
9	C₇×C₅₃	#595	1	1	yes	characteristic, complemented, Hall
10	C₇×D₁₇	—	53	1	no	—
11	#6157	—	17	1	no	Hall
12	C₇×C₁₇	#6157	1	1	yes	characteristic, complemented, Hall
13	D₅₃	—	17	1	no	—
14	#595	—	53	1	no	Hall
15	C₅₃	C₇×#595	1	1	yes	characteristic, complemented, Sylow
16	D₁₇	—	53	1	no	—
17	C₄×C₇	—	901	1	no	Hall
18	C₁₇	C₇×#6157	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₇	—	901	1	no	—
20	C₇	#16813357	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	—	901	1	no	Sylow
22	C₂	—	901	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.