Subgroups — C₂×C₃×3₋¹⁺² #4213

Order 162.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₂×C₃³	C₃	1	1	yes	maximal, characteristic
3	C₂×3₋¹⁺²	C₃	1	9	yes	maximal, direct product factor
4	C₂×C₃×C₉	C₃	1	3	yes	maximal, complemented
5	C₃³	C₂×C₃	1	1	yes	characteristic
6	3₋¹⁺²	C₂×C₃	1	9	yes	direct product factor
7	C₃×C₉	C₂×C₃	1	3	yes	complemented
8	C₂×C₃²	—	3	3	no	—
9	C₂×C₃²	C₃²	1	3	yes	—
10	C₂×C₃²	C₃²	1	1	yes	characteristic
11	C₂×C₉	C₃²	1	9	yes	complemented
12	C₃²	—	3	3	no	—
13	C₃²	C₂×C₃²	1	3	yes	—
14	C₃²	C₂×C₃²	1	1	yes	characteristic
15	C₉	C₂×C₃²	1	9	yes	complemented
16	C₂×C₃	—	3	3	no	—
17	C₂×C₃	3₋¹⁺²	1	3	yes	direct product factor
18	C₂×C₃	C₃³	1	1	yes	characteristic
19	C₃	—	3	3	no	—
20	C₃	C₂×3₋¹⁺²	1	3	yes	direct product factor
21	C₃	C₂×C₃³	1	1	yes	characteristic
22	C₂	C₃×3₋¹⁺²	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, socle	C₂×C₃²	C₃²
commutator, Frattini, cosocle	C₃	C₂×C₃³
prime radical	C₂×C₃³	C₃
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₂×C₃² ◁ G

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.