Subgroups — #15692425

Order 3249.

9 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₆₁⋊C₃	C₃	1	1	yes	maximal, characteristic
2	C₃₆₁	C₉	1	1	yes	characteristic, complemented, Sylow
3	#4296	—	19	1	no	maximal
4	C₁₉⋊C₃	—	19	1	no	—
5	C₁₉	#4296	1	1	yes	characteristic
6	C₉	—	361	1	no	Sylow
7	C₃	—	361	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₃₆₁	C₉
Frattini, socle	C₁₉	#4296
prime radical, cosocle	C₃₆₁⋊C₃	C₃
LCS	G ▷ C₃₆₁
UCS	C₁

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

N	H ≅ G/N	type
2. C₃₆₁	C₉	semidirect

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

subgroup	index
C₃₆₁⋊C₃	3
#4296	19