Subgroups — C₃⋊D₃² #66477

Order 324.

356 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₃⋊(C₃⋊D₃))	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×C₃⋊D₃	C₂	1	2	yes	maximal, complemented
3	D₃×C₃⋊D₃	—	3	8	no	maximal
4	C₃⁴	C₂²	1	1	yes	characteristic, complemented, Sylow
5	C₃⋊(C₃⋊D₃)	—	3	8	no	—
6	C₃⋊(C₃⋊D₃)	—	6	16	no	—
7	C₃×C₃⋊D₃	D₃	1	8	yes	complemented
8	C₃²×D₃	—	3	8	no	—
9	C₂×C₃⋊D₃	—	9	2	no	—
10	D₃²	—	9	16	no	—
11	C₃³	—	2	16	no	—
12	C₃³	C₂×D₃	1	8	yes	complemented
13	C₂×C₃²	—	9	2	no	—
14	C₃⋊D₃	—	9	2	no	—
15	C₃⋊D₃	—	9	16	no	—
16	C₃⋊D₃	—	18	32	no	—
17	C₃⋊D₃	—	18	24	no	—
18	C₃⋊D₃	C₃⋊D₃	1	2	yes	direct product factor
19	C₃×D₃	—	3	32	no	—
20	C₂×D₃	—	27	8	no	—
21	C₃²	—	2	24	no	—
22	C₃²	—	2	32	no	—
23	C₃²	D₃²	1	16	yes	complemented
24	C₃²	C₂×C₃⋊D₃	1	2	yes	complemented
25	C₂×C₃	—	9	8	no	—
26	D₃	—	3	8	no	—
27	D₃	—	27	8	no	—
28	D₃	—	54	16	no	—
29	C₂²	—	81	1	no	Sylow
30	C₃	—	2	16	no	—
31	C₃	D₃×C₃⋊D₃	1	8	yes	complemented
32	C₂	—	9	2	no	—
33	C₂	—	81	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃⁴	C₂²
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.