Subgroups — #4207⋊C₂ #66433

Order 324.

71 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#4208	C₂	1	1	yes	maximal, characteristic, complemented
2	#4207	C₂	1	2	yes	maximal, complemented
3	((C₃⋊D₃)⋊C₃)⋊C₂	—	3	1	no	maximal
4	D₃×D₉	—	3	2	no	maximal
5	#737	C₂²	1	1	yes	characteristic, complemented, Sylow
6	#272	D₃	1	1	yes	characteristic
7	C₃⋊D₉	D₃	1	2	yes	complemented
8	AGL(1,ℤ/9)	—	6	2	no	—
9	(C₃⋊D₃)⋊C₃	—	3	2	no	—
10	D₃×C₉	—	3	2	no	—
11	D₃×C₉	—	6	1	no	—
12	C₃×D₉	—	3	2	no	—
13	D₃²	—	9	2	no	—
14	C₂×D₉	—	9	1	no	—
15	3₋¹⁺²	—	2	2	no	—
16	3₋¹⁺²	—	4	1	no	—
17	H(3,𝔽₃)	C₂×D₃	1	1	yes	characteristic
18	C₃×C₉	—	2	1	no	—
19	C₃×C₉	C₂×D₃	1	2	yes	complemented
20	C₃⋊D₃	—	3	2	no	—
21	C₃×D₃	—	3	2	no	—
22	C₃×D₃	—	6	1	no	—
23	C₃×D₃	—	9	2	no	—
24	C₂×C₉	—	9	1	no	—
25	D₉	—	3	2	no	—
26	D₉	—	6	2	no	—
27	C₂×D₃	—	27	2	no	—
28	C₂×D₃	—	27	1	no	—
29	C₃²	—	2	1	no	—
30	C₃²	D₃²	1	2	yes	—
31	C₉	—	2	2	no	—
32	C₉	—	4	1	no	—
33	C₉	D₃²	1	1	yes	characteristic
34	C₂×C₃	—	9	1	no	—
35	C₂×C₃	—	27	2	no	—
36	D₃	—	3	2	no	—
37	D₃	—	6	1	no	—
38	D₃	—	9	2	no	—
39	D₃	—	27	2	no	—
40	C₂²	—	81	1	no	Sylow
41	C₃	—	3	2	no	—
42	C₃	—	6	1	no	—
43	C₃	#1113	1	1	yes	characteristic
44	C₂	—	9	1	no	—
45	C₂	—	27	2	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	#737	C₂²
Frattini, socle	C₃	#1113
LCS	G ▷ #737
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.