Subgroups — C₃×C₁₇×Dic₇ #13083604

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	C₁₇×Dic₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₇×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₁₇	C₂×C₃	1	1	yes	characteristic
5	C₃×C₄×C₁₇	—	7	1	no	maximal, Hall
6	C₇×C₁₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₁₇	D₇	1	1	yes	characteristic
8	C₃×Dic₇	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₄×C₁₇	—	7	1	no	Hall
10	C₃×C₁₇	Dic₇	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₃×C₇	C₂×C₁₇	1	1	yes	characteristic
12	C₂×C₁₇	C₃×D₇	1	1	yes	characteristic
13	Dic₇	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₇	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
15	C₁₇	C₃×Dic₇	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₇	C₂×C₃×C₁₇	1	1	yes	characteristic
17	C₃×C₄	—	7	1	no	Hall
18	C₇	C₃×C₄×C₁₇	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃	D₇×C₁₇	1	1	yes	characteristic
20	C₄	—	7	1	no	Sylow
21	C₃	C₁₇×Dic₇	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₃×D₇×C₁₇	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.