Subgroups — #4178⋊C₂ #66349

Order 324.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#4185	C₂	1	1	yes	maximal, characteristic, complemented
2	#4179	C₂	1	1	yes	maximal, characteristic, complemented
3	#4178	C₂	1	1	yes	maximal, characteristic, complemented
4	((C₃⋊D₃)⋊C₃)⋊C₂	—	3	1	no	maximal
5	D₃×D₉	—	3	1	no	maximal
6	#732	C₂²	1	1	yes	characteristic, complemented, Sylow
7	#272	D₃	1	1	yes	characteristic, complemented
8	C₃⋊D₉	D₃	1	1	yes	characteristic, complemented
9	(C₃⋊D₃)⋊C₃	—	3	1	no	—
10	(C₃⋊D₃)⋊C₃	—	3	1	no	—
11	(C₃⋊D₃)⋊C₃	—	6	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	H(3,𝔽₃)	—	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	—	6	1	no	—
23	C₃×D₃	—	3	1	no	—
24	C₃×D₃	—	9	1	no	—
25	C₃×D₃	—	9	1	no	—
26	C₃×D₃	—	9	1	no	—
27	C₂×C₉	—	9	1	no	—
28	D₉	—	3	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	—	6	1	no	—
35	C₃²	D₃²	1	1	yes	characteristic
36	C₉	—	3	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	D₃	—	54	1	no	—
47	C₂²	—	81	1	no	Sylow
48	C₃	—	3	1	no	—
49	C₃	—	9	1	no	—
50	C₃	—	18	1	no	—
51	C₃	((C₃⋊D₃)⋊C₃)⋊C₂	1	1	yes	characteristic
52	C₂	—	9	1	no	—
53	C₂	—	27	1	no	—
54	C₂	—	27	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	#732	C₂²
Frattini	C₃²	D₃²
socle	C₃	((C₃⋊D₃)⋊C₃)⋊C₂
LCS	G ▷ #732
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.