Subgroups — C₃⋊(C₃⋊(C₃⋊D₃)) #4218

Order 162.

424 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁴	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃⋊(C₃⋊D₃)	—	3	40	no	maximal
3	C₃³	D₃	1	40	yes	complemented
4	C₃⋊D₃	—	9	130	no	—
5	C₃²	C₃⋊D₃	1	130	yes	complemented
6	D₃	—	27	40	no	—
7	C₃	C₃⋊(C₃⋊D₃)	1	40	yes	complemented
8	C₂	—	81	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃⁴	C₂
LCS	G ▷ C₃⁴
UCS	C₁

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.

subgroup	index
C₃⁴	2
C₃⋊(C₃⋊D₃)	3