Subgroups — #32913541

Order 18369.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₁₅₇	C₃	1	1	yes	maximal, characteristic
2	C₁₃×C₁₅₇	C₉	1	1	yes	characteristic, complemented, Hall
3	C₁₅₇⋊C₉	—	13	1	no	maximal, Hall
4	C₃×C₁₅₇	C₁₃⋊C₃	1	1	yes	characteristic
5	C₁₅₇	C₁₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
6	C₁₃⋊C₉	—	157	1	no	maximal, Hall
7	C₃×C₁₃	C₁₅₇⋊C₃	1	1	yes	characteristic
8	C₁₃	C₁₅₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
9	C₉	—	2041	1	no	Sylow
10	C₃	#20259404	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₃	#20259404
commutator, hypocenter	C₁₃×C₁₅₇	C₉
Fitting, socle, prime radical, cosocle	C₃×C₁₃×C₁₅₇	C₃
LCS	G ▷ C₁₃×C₁₅₇
UCS	C₁ ◁ C₃

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.