Subgroups — C₃×#10624497 #14550879

Order 2187.

458 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#6866	C₃	1	4	yes	maximal
2	#10624497	C₃	1	9	yes	maximal, direct product factor
3	C₃⁵	C₃²	1	1	yes	characteristic
4	C₃×C₃²⋊C₉	—	3	4	no	—
5	#6866	—	3	8	no	—
6	#6866	C₃²	1	12	yes	—
7	C₃⁴	—	3	4	no	—
8	C₃⁴	—	3	8	no	—
9	C₃⁴	—	9	9	no	—
10	C₃⁴	H(3,𝔽₃)	1	2	yes	—
11	C₃⁴	H(3,𝔽₃)	1	1	yes	characteristic
12	C₃⁴	C₃³	1	1	yes	characteristic
13	C₃²×C₉	—	9	4	no	—
14	C₃²⋊C₉	—	3	12	no	—
15	C₃²⋊C₉	—	9	8	no	—
16	C₃³	—	3	8	no	—
17	C₃³	—	3	4	no	—
18	C₃³	—	9	3	no	—
19	C₃³	—	9	36	no	—
20	C₃³	—	9	6	no	—
21	C₃³	—	9	3	no	—
22	C₃³	—	9	72	no	—
23	C₃³	—	9	8	no	—
24	C₃³	—	9	1	no	—
25	C₃³	#731	1	4	yes	—
26	C₃³	#731	1	8	yes	—
27	C₃³	C₃×H(3,𝔽₃)	1	1	yes	characteristic
28	C₃×C₉	—	9	12	no	—
29	C₃×C₉	—	27	12	no	—
30	C₃²	—	3	12	no	—
31	C₃²	—	9	8	no	—
32	C₃²	—	9	1	no	—
33	C₃²	—	9	24	no	—
34	C₃²	—	9	12	no	—
35	C₃²	—	9	72	no	—
36	C₃²	—	9	2	no	—
37	C₃²	—	9	1	no	—
38	C₃²	—	9	9	no	—
39	C₃²	#6862	1	8	yes	—
40	C₃²	#6862	1	1	yes	characteristic
41	C₃²	C₃×#731	1	4	yes	—
42	C₉	—	27	12	no	—
43	C₃	—	3	4	no	—
44	C₃	—	3	8	no	—
45	C₃	—	9	6	no	—
46	C₃	—	9	3	no	—
47	C₃	#10624497	1	3	yes	direct product factor
48	C₃	C₃×#6862	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃²	#6862
commutator, Frattini, cosocle	C₃⁴	C₃³
prime radical	C₃⁵	C₃²
LCS	G ▷ C₃⁴ ▷ C₃³ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃² ◁ C₃⁴ ◁ C₃⁵ ◁ G
LECS	G ▷ C₃⁴ ▷ C₃³ ▷ C₃ ▷ C₁

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

N	H ≅ G/N	type
2. #10624497	C₃	direct (N × H)
47. C₃	#10624497	direct (N × H)

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

subgroup	index
C₃×#6866	3
#10624497	3