Subgroups — C₃×D₃² #1111

Order 108.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×D₃	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×D₃	—	3	2	no	maximal
4	D₃²	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₃³	C₂²	1	1	yes	characteristic, complemented, Sylow
6	C₂×C₃²	—	3	2	no	—
7	C₃⋊D₃	C₂×C₃	1	1	yes	characteristic, complemented
8	C₃×D₃	—	2	2	no	—
9	C₃×D₃	—	3	2	no	—
10	C₃×D₃	—	6	1	no	—
11	C₃×D₃	D₃	1	2	yes	direct product factor
12	C₃×D₃	C₂×C₃	1	2	yes	complemented
13	C₂²×C₃	—	9	1	no	—
14	C₂×D₃	—	3	2	no	—
15	C₃²	—	2	1	no	—
16	C₃²	—	2	2	no	—
17	C₃²	—	4	1	no	—
18	C₃²	C₂×D₃	1	2	yes	complemented
19	C₃²	C₂²×C₃	1	1	yes	characteristic, complemented
20	C₂×C₃	—	3	2	no	—
21	C₂×C₃	—	3	2	no	—
22	C₂×C₃	—	6	2	no	—
23	C₂×C₃	—	9	1	no	—
24	D₃	—	3	2	no	—
25	D₃	—	6	1	no	—
26	D₃	C₃×D₃	1	2	yes	direct product factor
27	C₂²	—	9	1	no	Sylow
28	C₃	—	2	1	no	—
29	C₃	—	2	2	no	—
30	C₃	—	4	1	no	—
31	C₃	D₃²	1	1	yes	characteristic, direct product factor
32	C₃	C₂×C₃×D₃	1	2	yes	complemented
33	C₂	—	3	2	no	—
34	C₂	—	9	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₃²
commutator, cosocle, hypocenter	C₃²	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃³	C₂²
LCS	G ▷ C₃²
UCS	C₁ ◁ C₃

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.