Subgroups — #36346367

Order 21897.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20300457	C₃	1	1	yes	maximal, characteristic
2	C₃×C₈₁₁	C₉	1	1	yes	characteristic
3	C₈₁₁	C₂₇	1	1	yes	characteristic, complemented, Sylow
4	C₂₇	—	811	1	no	maximal, Sylow
5	C₉	—	811	1	no	—
6	C₃	#20300459	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₃	#20300459
commutator, hypocenter	C₈₁₁	C₂₇
Fitting, socle, prime radical	C₃×C₈₁₁	C₉
cosocle	#20300457	C₃
LCS	G ▷ C₈₁₁
UCS	C₁ ◁ C₃

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

N	H ≅ G/N	type
3. C₈₁₁	C₂₇	semidirect

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

subgroup	index
#20300457	3
C₂₇	811