Subgroups — C₃×C₂₁₆₁⋊C₃ #34085557

Order 19449.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₁₆₁	C₃	1	1	yes	maximal, characteristic, complemented
2	C₂₁₆₁⋊C₃	C₃	1	3	yes	maximal, direct product factor
3	C₂₁₆₁	C₃²	1	1	yes	characteristic, complemented, Sylow
4	C₃²	—	2161	1	no	maximal, Sylow
5	C₃	—	2161	3	no	—
6	C₃	C₂₁₆₁⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₃	C₂₁₆₁⋊C₃
commutator, cosocle, hypocenter	C₂₁₆₁	C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₂₁₆₁	C₃
LCS	G ▷ C₂₁₆₁
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.