Subgroups — C₉×D₁₃₆₁ #37587720

Order 24498.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₃₆₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₁₃₆₁	C₃	1	1	yes	maximal, characteristic
3	C₃×C₁₃₆₁	C₂×C₃	1	1	yes	characteristic
4	D₁₃₆₁	C₉	1	1	yes	characteristic, direct product factor, Hall
5	C₁₃₆₁	C₂×C₉	1	1	yes	characteristic, complemented, Sylow
6	C₂×C₉	—	1361	1	no	maximal, Hall
7	C₉	D₁₃₆₁	1	1	yes	characteristic, direct product factor, Sylow
8	C₂×C₃	—	1361	1	no	—
9	C₃	C₃×D₁₃₆₁	1	1	yes	characteristic
10	C₂	—	1361	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.