Subgroups — #14548201

Order 2187.

534 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₉²	C₃	1	1	yes	maximal, characteristic, complemented
2	#10624812	C₃	1	8	yes	maximal, complemented
3	#10624811	C₃	1	4	yes	maximal
4	C₃³×C₉	C₃²	1	4	yes	—
5	#6891	C₃²	1	8	yes	—
6	C₃²⋊H(3,𝔽₃)	C₃²	1	1	yes	characteristic
7	C₃×C₉²	—	3	12	no	—
8	3₋¹⁺²⋊C₉	—	3	24	no	—
9	H(3,𝔽₃)⋊C₉	—	3	12	no	—
10	C₃⁴	C₃³	1	1	yes	characteristic
11	C₃×3₋¹⁺²	—	3	8	no	—
12	C₃×H(3,𝔽₃)	—	3	4	no	—
13	C₃²×C₉	—	3	8	no	—
14	C₃²×C₉	—	3	4	no	—
15	C₃²×C₉	—	3	36	no	—
16	C₃²×C₉	H(3,𝔽₃)	1	12	yes	—
17	C₃²⋊C₉	—	3	8	no	—
18	C₃²⋊C₉	—	3	16	no	—
19	C₉²	—	3	27	no	—
20	C₃³	—	3	12	no	—
21	C₃³	—	9	1	no	—
22	C₃³	C₃×H(3,𝔽₃)	1	4	yes	—
23	3₋¹⁺²	—	9	24	no	—
24	H(3,𝔽₃)	—	9	12	no	—
25	C₃×C₉	—	3	72	no	—
26	C₃×C₉	—	3	12	no	—
27	C₃×C₉	—	3	36	no	—
28	C₃×C₉	—	3	36	no	—
29	C₃×C₉	—	9	8	no	—
30	C₃²	—	3	27	no	—
31	C₃²	—	3	8	no	—
32	C₃²	—	3	4	no	—
33	C₃²	—	27	4	no	—
34	C₃²	C₃²⋊H(3,𝔽₃)	1	1	yes	characteristic
35	C₃²	#6908	1	12	yes	—
36	C₉	—	3	36	no	—
37	C₉	—	27	8	no	—
38	C₃	—	3	12	no	—
39	C₃	—	81	1	no	—
40	C₃	#10624734	1	4	yes	—

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

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

N	H ≅ G/N	type
1. C₃²×C₉²	C₃	semidirect
2. #10624812	C₃	semidirect

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