Subgroups — C₃²×C₃⋊D₃ #4216

Order 162.

160 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	C₃	1	4	yes	maximal, direct product factor
3	C₃²×D₃	—	3	4	no	maximal
4	C₃³	—	2	16	no	—
5	C₃³	D₃	1	4	yes	complemented
6	C₃³	C₂×C₃	1	4	yes	complemented
7	C₂×C₃²	—	9	1	no	—
8	C₃⋊D₃	C₃²	1	1	yes	characteristic, direct product factor
9	C₃×D₃	—	3	16	no	—
10	C₃²	—	2	24	no	—
11	C₃²	—	2	16	no	—
12	C₃²	—	2	16	no	—
13	C₃²	C₃×D₃	1	16	yes	complemented
14	C₃²	C₃⋊D₃	1	1	yes	characteristic, direct product factor
15	C₃²	C₂×C₃²	1	1	yes	characteristic, complemented
16	C₂×C₃	—	9	4	no	—
17	D₃	—	3	4	no	—
18	C₃	—	2	16	no	—
19	C₃	C₃²×D₃	1	4	yes	complemented
20	C₃	C₃×C₃⋊D₃	1	4	yes	direct product factor
21	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃⁴	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₃²

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.