Subgroups — C₇×Dic₅₁ #13083607

Order 1428.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇×C₁₇	C₂	1	1	yes	maximal, characteristic
2	C₇×Dic₁₇	—	3	1	no	maximal, Hall
3	C₃×C₇×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₁₇	D₃	1	1	yes	characteristic
5	Dic₅₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×C₁₇	Dic₃	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₁₇	C₂×C₇	1	1	yes	characteristic
8	C₇×Dic₃	—	17	1	no	maximal, Hall
9	Dic₁₇	—	3	1	no	Hall
10	C₃×C₁₇	C₄×C₇	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₇	D₁₇	1	1	yes	characteristic
12	C₂×C₁₇	D₃×C₇	1	1	yes	characteristic
13	C₄×C₇	—	51	1	no	Hall
14	C₃×C₇	Dic₁₇	1	1	yes	characteristic, complemented, Hall
15	C₁₇	C₇×Dic₃	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₇	D₅₁	1	1	yes	characteristic
17	Dic₃	—	17	1	no	Hall
18	C₇	Dic₅₁	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₃	C₇×D₁₇	1	1	yes	characteristic
20	C₄	—	51	1	no	Sylow
21	C₃	C₇×Dic₁₇	1	1	yes	characteristic, complemented, Sylow
22	C₂	C₇×D₅₁	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.