Subgroups — #44540889

Order 31761.

6 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₅₂₉⋊C₃	C₃	1	1	yes	maximal, characteristic
2	C₃₅₂₉	C₉	1	1	yes	characteristic, complemented, Sylow
3	C₉	—	3529	1	no	maximal, Sylow
4	C₃	—	3529	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃₅₂₉	C₉
prime radical, cosocle	C₃₅₂₉⋊C₃	C₃
LCS	G ▷ C₃₅₂₉
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₃₅₂₉	C₉	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃₅₂₉⋊C₃	3
C₉	3529