Subgroups — C₁₇×Dic₂₄₇ #30680988

Order 16796.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×C₁₇×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₃×C₁₇×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₇×Dic₁₉	—	13	1	no	maximal, Hall
4	Dic₂₄₇	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₇×Dic₁₃	—	19	1	no	maximal, Hall
6	C₂×C₁₇×C₁₉	D₁₃	1	1	yes	characteristic
7	C₂×C₁₃×C₁₉	C₂×C₁₇	1	1	yes	characteristic
8	C₂×C₁₃×C₁₇	D₁₉	1	1	yes	characteristic
9	C₁₇×C₁₉	Dic₁₃	1	1	yes	characteristic, complemented, Hall
10	C₁₃×C₁₉	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
11	C₁₃×C₁₇	Dic₁₉	1	1	yes	characteristic, complemented, Hall
12	Dic₁₉	—	13	1	no	Hall
13	C₄×C₁₇	—	247	1	no	Hall
14	Dic₁₃	—	19	1	no	Hall
15	C₂×C₁₉	C₁₇×D₁₃	1	1	yes	characteristic
16	C₂×C₁₇	D₂₄₇	1	1	yes	characteristic
17	C₂×C₁₃	C₁₇×D₁₉	1	1	yes	characteristic
18	C₁₉	C₁₇×Dic₁₃	1	1	yes	characteristic, complemented, Sylow
19	C₁₇	Dic₂₄₇	1	1	yes	characteristic, direct product factor, Sylow
20	C₁₃	C₁₇×Dic₁₉	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	247	1	no	Sylow
22	C₂	C₁₇×D₂₄₇	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.