Subgroups — #14550797

Order 2187.

426 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624885	C₃	1	4	yes	maximal
2	H(3,ℤ/9)	C₃	1	9	yes	maximal, complemented
3	C₃²×3₋¹⁺²	C₃²	1	1	yes	characteristic
4	#6896	—	3	36	no	—
5	#6895	—	3	8	no	—
6	#6891	—	3	4	no	—
7	#6887	C₃²	1	12	yes	—
8	C₃⁴	H(3,𝔽₃)	1	1	yes	characteristic
9	C₃×3₋¹⁺²	—	3	12	no	—
10	C₃×3₋¹⁺²	—	3	12	no	—
11	C₃²×C₉	H(3,𝔽₃)	1	2	yes	—
12	C₃²×C₉	C₃³	1	1	yes	characteristic
13	C₉⋊C₉	—	3	72	no	—
14	C₉⋊C₉	—	3	24	no	—
15	C₃²⋊C₉	—	3	24	no	—
16	C₃²⋊C₉	—	3	12	no	—
17	C₉²	3₋¹⁺²	1	36	yes	complemented
18	C₃³	—	3	4	no	—
19	C₃³	—	27	1	no	—
20	C₃³	C₃×H(3,𝔽₃)	1	1	yes	characteristic
21	3₋¹⁺²	—	9	9	no	—
22	3₋¹⁺²	—	27	12	no	—
23	C₃×C₉	—	3	36	no	—
24	C₃×C₉	—	3	8	no	—
25	C₃×C₉	C₃×3₋¹⁺²	1	12	yes	—
26	C₃²	—	9	1	no	—
27	C₃²	—	9	4	no	—
28	C₃²	—	9	8	no	—
29	C₃²	—	9	1	no	—
30	C₃²	#6891	1	4	yes	—
31	C₉	—	9	36	no	—
32	C₉	—	9	2	no	—
33	C₉	#6900	1	9	yes	—
34	C₃	—	3	4	no	—
35	C₃	—	27	1	no	—
36	C₃	#10624571	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃	#10624571
commutator, Frattini, cosocle	C₃²×C₉	C₃³
prime radical	C₃⁴	H(3,𝔽₃)
LCS	G ▷ C₃²×C₉ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃ ◁ C₃²×C₉ ◁ G
LECS	G ▷ C₃²×C₉ ▷ C₃ ▷ C₁

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

N	H ≅ G/N	type
2. H(3,ℤ/9)	C₃	semidirect
17. C₉²	3₋¹⁺²	semidirect

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

subgroup	index
#10624885	3
H(3,ℤ/9)	3