Subgroups — C₃×#10624576 #14552166

Order 2187.

962 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
2	#10624576	C₃	1	27	yes	maximal, direct product factor
3	C₃×#6855	C₃	1	9	yes	maximal
4	C₃×#6855	C₃	1	2	yes	maximal
5	C₃×#6855	C₃	1	1	yes	maximal, characteristic
6	C₃³×C₉	C₃²	1	6	yes	—
7	C₃³×C₉	C₃²	1	3	yes	—
8	C₃³×C₉	C₃²	1	3	yes	—
9	C₃³×C₉	C₃²	1	1	yes	characteristic
10	C₃×C₉⋊C₉	—	3	9	no	—
11	C₃×C₉⋊C₉	C₃²	1	9	yes	—
12	#6855	C₃²	1	81	yes	—
13	#6855	C₃²	1	18	yes	—
14	#6855	C₃²	1	9	yes	—
15	C₃⁴	C₃³	1	1	yes	characteristic
16	C₃²×C₉	—	3	6	no	—
17	C₃²×C₉	—	3	3	no	—
18	C₃²×C₉	—	3	9	no	—
19	C₃²×C₉	—	3	18	no	—
20	C₃²×C₉	—	3	54	no	—
21	C₃²×C₉	—	3	9	no	—
22	C₃²×C₉	—	3	27	no	—
23	C₃²×C₉	—	3	27	no	—
24	C₃²×C₉	3₋¹⁺²	1	9	yes	—
25	C₃²×C₉	C₃³	1	18	yes	—
26	C₃²×C₉	C₃³	1	9	yes	—
27	C₃²×C₉	C₃³	1	9	yes	—
28	C₃²×C₉	C₃³	1	3	yes	—
29	C₉⋊C₉	—	3	27	no	—
30	C₃³	C₃×3₋¹⁺²	1	3	yes	—
31	C₃³	#737	1	6	yes	—
32	C₃³	#737	1	3	yes	—
33	C₃³	#737	1	27	yes	—
34	C₃³	C₃⁴	1	1	yes	characteristic
35	C₃×C₉	—	3	6	no	—
36	C₃×C₉	—	3	3	no	—
37	C₃×C₉	—	3	27	no	—
38	C₃×C₉	—	3	9	no	—
39	C₃×C₉	—	3	18	no	—
40	C₃×C₉	—	3	54	no	—
41	C₃×C₉	—	3	9	no	—
42	C₃×C₉	—	3	27	no	—
43	C₃×C₉	—	3	27	no	—
44	C₃×C₉	—	9	54	no	—
45	C₃×C₉	—	9	27	no	—
46	C₃×C₉	—	9	27	no	—
47	C₃×C₉	C₃×3₋¹⁺²	1	9	yes	—
48	C₃²	#6895	1	9	yes	—
49	C₃²	#6897	1	54	yes	—
50	C₃²	#6898	1	27	yes	—
51	C₃²	#6899	1	27	yes	—
52	C₃²	C₃²×3₋¹⁺²	1	1	yes	characteristic
53	C₃²	C₃×#737	1	2	yes	—
54	C₃²	C₃×#737	1	1	yes	characteristic
55	C₃²	C₃×#737	1	9	yes	—
56	C₉	—	3	9	no	—
57	C₉	—	9	18	no	—
58	C₉	—	9	9	no	—
59	C₉	—	9	9	no	—
60	C₃	#10624576	1	27	yes	direct product factor
61	C₃	C₃×#6895	1	1	yes	characteristic
62	C₃	C₃×#6897	1	6	yes	—
63	C₃	C₃×#6898	1	3	yes	—
64	C₃	C₃×#6899	1	3	yes	—

	subgroup	G/H
center, socle, prime radical	C₃⁴	C₃³
commutator, Frattini, cosocle	C₃³	C₃⁴
LCS	G ▷ C₃³ ▷ C₁
UCS	C₁ ◁ C₃⁴ ◁ G
LECS	G ▷ C₃³ ▷ C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. #10624576	C₃	direct (N × H)
60. C₃	#10624576	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×C₉⋊C₉	3
#10624576	3
C₃×#6855	3

Subgroups — C3×#10624576 #14552166

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10624576 #14552166