Subgroups — C₃⋊(C₃⋊D₉) #4209

Order 162.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₉	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃⋊(C₃⋊D₃)	—	3	1	no	maximal
3	C₃⋊D₉	—	3	12	no	maximal
4	C₃³	D₃	1	1	yes	characteristic
5	C₃×C₉	D₃	1	12	yes	complemented
6	C₃⋊D₃	—	9	9	no	—
7	C₃⋊D₃	—	9	4	no	—
8	D₉	—	9	9	no	—
9	C₃²	D₉	1	9	yes	complemented
10	C₃²	C₃⋊D₃	1	4	yes	—
11	C₉	C₃⋊D₃	1	9	yes	complemented
12	D₃	—	27	12	no	—
13	D₃	—	27	1	no	—
14	C₃	C₃⋊D₉	1	12	yes	complemented
15	C₃	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
16	C₂	—	81	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃²×C₉	C₂
Frattini	C₃	C₃⋊(C₃⋊D₃)
socle	C₃³	D₃
LCS	G ▷ C₃²×C₉
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.