Subgroups — #14550774

Order 2187.

190 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624692	C₃	1	4	yes	maximal
2	#10624470	C₃	1	8	yes	maximal, complemented
3	H(3,ℤ/9)	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃²×3₋¹⁺²	C₃²	1	1	yes	characteristic
5	#6887	C₃²	1	4	yes	—
6	#6887	C₃²	1	8	yes	—
7	#6868	—	3	4	no	—
8	#6867	—	3	4	no	—
9	#6866	—	3	4	no	—
10	C₃⁴	H(3,𝔽₃)	1	1	yes	characteristic
11	C₃×3₋¹⁺²	—	3	4	no	—
12	C₃×3₋¹⁺²	—	3	8	no	—
13	C₃²×C₉	H(3,𝔽₃)	1	2	yes	—
14	C₃²×C₉	C₃³	1	1	yes	characteristic
15	C₉⋊C₉	—	3	8	no	—
16	C₉⋊C₉	—	3	8	no	—
17	C₉⋊C₉	—	3	8	no	—
18	C₃²⋊C₉	—	3	4	no	—
19	C₃²⋊C₉	—	3	8	no	—
20	C₉²	—	3	4	no	—
21	C₉²	—	3	8	no	—
22	C₃³	—	3	4	no	—
23	C₃³	—	27	1	no	—
24	C₃³	C₃×H(3,𝔽₃)	1	1	yes	characteristic
25	3₋¹⁺²	—	9	1	no	—
26	3₋¹⁺²	—	9	8	no	—
27	C₃×C₉	—	3	8	no	—
28	C₃×C₉	—	9	4	no	—
29	C₃×C₉	—	9	8	no	—
30	C₃×C₉	#737	1	4	yes	—
31	C₃×C₉	#737	1	8	yes	—
32	C₃²	—	9	1	no	—
33	C₃²	—	9	1	no	—
34	C₃²	—	27	4	no	—
35	C₃²	#6893	1	4	yes	—
36	C₉	—	9	2	no	—
37	C₉	—	27	4	no	—
38	C₉	—	27	8	no	—
39	C₉	#6897	1	1	yes	characteristic
40	C₉	#6897	1	8	yes	—
41	C₃	—	3	4	no	—
42	C₃	—	27	1	no	—
43	C₃	#10624568	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃	#10624568
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. #10624470	C₃	semidirect
3. H(3,ℤ/9)	C₃	semidirect

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