Subgroups — C₃×#10624564 #14552152

Order 2187.

3536 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
2	C₃²×C₃²⋊C₉	C₃	1	12	yes	maximal, complemented
3	#10624564	C₃	1	27	yes	maximal, direct product factor
4	C₃⁵	C₃²	1	4	yes	—
5	C₃²×H(3,𝔽₃)	—	3	36	no	—
6	C₃²×H(3,𝔽₃)	C₃²	1	9	yes	—
7	C₃³×C₉	C₃²	1	9	yes	—
8	C₃×C₃²⋊C₉	—	3	108	no	—
9	C₃×C₃²⋊C₉	C₃²	1	108	yes	complemented
10	C₃⁴	—	3	36	no	—
11	C₃⁴	—	3	108	no	—
12	C₃⁴	H(3,𝔽₃)	1	36	yes	—
13	C₃⁴	C₃³	1	12	yes	—
14	C₃⁴	C₃³	1	1	yes	characteristic
15	C₃×H(3,𝔽₃)	—	3	243	no	—
16	C₃×H(3,𝔽₃)	—	3	108	no	—
17	C₃²×C₉	—	3	108	no	—
18	C₃²×C₉	C₃³	1	27	yes	—
19	C₃²⋊C₉	—	3	324	no	—
20	C₃³	—	3	36	no	—
21	C₃³	—	3	108	no	—
22	C₃³	—	3	108	no	—
23	C₃³	—	3	324	no	—
24	C₃³	—	9	324	no	—
25	C₃³	C₃×H(3,𝔽₃)	1	36	yes	—
26	C₃³	C₃×H(3,𝔽₃)	1	12	yes	—
27	C₃³	#737	1	27	yes	—
28	C₃³	C₃⁴	1	1	yes	characteristic
29	H(3,𝔽₃)	—	3	243	no	—
30	C₃×C₉	—	3	108	no	—
31	C₃×C₉	—	9	81	no	—
32	C₃²	—	3	36	no	—
33	C₃²	—	3	108	no	—
34	C₃²	—	9	324	no	—
35	C₃²	—	9	108	no	—
36	C₃²	C₃²⋊H(3,𝔽₃)	1	9	yes	—
37	C₃²	#6893	1	108	yes	—
38	C₃²	C₃²×H(3,𝔽₃)	1	4	yes	—
39	C₃²	C₃×#737	1	9	yes	—
40	C₉	—	9	27	no	—
41	C₃	—	9	36	no	—
42	C₃	#10624564	1	27	yes	direct product factor
43	C₃	C₃×C₃²⋊H(3,𝔽₃)	1	1	yes	characteristic
44	C₃	C₃×#6893	1	12	yes	—

	subgroup	G/H
center, socle	C₃⁴	C₃³
commutator, Frattini, cosocle	C₃³	C₃⁴
prime radical	C₃³×H(3,𝔽₃)	C₃
LCS	G ▷ C₃³ ▷ C₁
UCS	C₁ ◁ C₃⁴ ◁ G
LECS	G ▷ C₃³ ▷ 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.