Subgroups — C₇×C₉×D₁₃₇ #31772113

Order 17262.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₉×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇×D₁₃₇	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇×C₁₃₇	C₂×C₃	1	1	yes	characteristic
4	C₉×D₁₃₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×D₁₃₇	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₉×C₁₃₇	C₂×C₇	1	1	yes	characteristic, complemented, Hall
7	C₇×C₁₃₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
8	C₃×D₁₃₇	C₃×C₇	1	1	yes	characteristic
9	C₃×C₁₃₇	C₂×C₃×C₇	1	1	yes	characteristic
10	D₁₃₇	C₇×C₉	1	1	yes	characteristic, direct product factor, Hall
11	C₁₃₇	C₂×C₇×C₉	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₇×C₉	—	137	1	no	maximal, Hall
13	C₇×C₉	D₁₃₇	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃×C₇	—	137	1	no	—
15	C₃×C₇	C₃×D₁₃₇	1	1	yes	characteristic
16	C₂×C₉	—	137	1	no	Hall
17	C₂×C₇	—	137	1	no	Hall
18	C₉	C₇×D₁₃₇	1	1	yes	characteristic, direct product factor, Sylow
19	C₇	C₉×D₁₃₇	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃	—	137	1	no	—
21	C₃	C₃×C₇×D₁₃₇	1	1	yes	characteristic
22	C₂	—	137	1	no	Sylow

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.