Subgroups — C₃⋊D₃ #47

Order 18.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	D₃	—	3	4	no	maximal
3	C₃	D₃	1	4	yes	complemented
4	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²	C₂
LCS	G ▷ C₃²
UCS	C₁

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

N	H ≅ G/N	type
1. C₃²	C₂	semidirect
3. C₃	D₃	semidirect

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

subgroup	index
C₃²	2
D₃	3