Subgroups — #4176⋊C₂ #66348

Order 324.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#4184	C₂	1	1	yes	maximal, characteristic, complemented
2	#4177	C₂	1	1	yes	maximal, characteristic, complemented
3	#4176	C₂	1	1	yes	maximal, characteristic, complemented
4	((C₃⋊D₃)⋊C₃)⋊C₂	—	3	1	no	maximal
5	D₃×D₉	—	3	1	no	maximal
6	#731	C₂²	1	1	yes	characteristic, complemented, Sylow
7	#272	D₃	1	1	yes	characteristic
8	C₃⋊D₉	D₃	1	1	yes	characteristic, complemented
9	AGL(1,ℤ/9)	—	6	1	no	—
10	(C₃⋊D₃)⋊C₃	—	3	1	no	—
11	(C₃⋊D₃)⋊C₃	—	3	1	no	—
12	D₃×C₉	—	3	1	no	—
13	C₃×D₉	—	3	1	no	—
14	D₃²	—	9	1	no	—
15	D₃²	—	9	1	no	—
16	C₂×D₉	—	9	1	no	—
17	3₋¹⁺²	—	2	1	no	—
18	H(3,𝔽₃)	C₂×D₃	1	1	yes	characteristic
19	C₃×C₉	C₂×D₃	1	1	yes	characteristic, complemented
20	C₃⋊D₃	—	3	1	no	—
21	C₃⋊D₃	—	3	1	no	—
22	C₃×D₃	—	3	1	no	—
23	C₃×D₃	—	9	1	no	—
24	C₃×D₃	—	9	1	no	—
25	C₃×D₃	—	9	1	no	—
26	C₂×C₉	—	9	1	no	—
27	D₉	—	3	1	no	—
28	D₉	—	6	1	no	—
29	D₉	—	9	1	no	—
30	C₂×D₃	—	27	1	no	—
31	C₂×D₃	—	27	1	no	—
32	C₂×D₃	—	27	1	no	—
33	C₃²	—	3	1	no	—
34	C₃²	D₃²	1	1	yes	characteristic
35	C₉	—	3	1	no	—
36	C₉	—	6	1	no	—
37	C₂×C₃	—	9	1	no	—
38	C₂×C₃	—	27	1	no	—
39	C₂×C₃	—	27	1	no	—
40	D₃	—	3	1	no	—
41	D₃	—	9	1	no	—
42	D₃	—	9	1	no	—
43	D₃	—	9	1	no	—
44	D₃	—	27	1	no	—
45	D₃	—	27	1	no	—
46	C₂²	—	81	1	no	Sylow
47	C₃	—	3	1	no	—
48	C₃	—	9	1	no	—
49	C₃	((C₃⋊D₃)⋊C₃)⋊C₂	1	1	yes	characteristic
50	C₂	—	9	1	no	—
51	C₂	—	27	1	no	—
52	C₂	—	27	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	#731	C₂²
Frattini	C₃²	D₃²
socle	C₃	((C₃⋊D₃)⋊C₃)⋊C₂
LCS	G ▷ #731
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.