Subgroups — #14550856

Order 2187.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#6868	C₃	1	3	yes	maximal
2	#10624549	C₃	1	1	yes	maximal, characteristic
3	#10624494	C₃	1	9	yes	maximal, complemented
4	C₃³×C₉	C₃²	1	1	yes	characteristic
5	C₃×C₃²⋊C₉	—	3	3	no	—
6	C₃×C₃²⋊C₉	—	3	1	no	—
7	#6868	—	3	6	no	—
8	#6868	C₃²	1	9	yes	—
9	#6855	—	3	2	no	—
10	#6855	C₃²	1	3	yes	—
11	C₃⁴	H(3,𝔽₃)	1	1	yes	characteristic
12	C₃²×C₉	—	3	3	no	—
13	C₃²×C₉	—	3	3	no	—
14	C₃²×C₉	—	3	6	no	—
15	C₃²×C₉	—	3	3	no	—
16	C₃²×C₉	—	9	3	no	—
17	C₃²×C₉	H(3,𝔽₃)	1	2	yes	—
18	C₃²×C₉	C₃³	1	1	yes	characteristic
19	C₃²⋊C₉	—	3	9	no	—
20	C₃²⋊C₉	—	9	3	no	—
21	C₃²⋊C₉	—	9	6	no	—
22	C₃³	—	9	1	no	—
23	C₃³	—	9	2	no	—
24	C₃³	#731	1	3	yes	—
25	C₃³	#732	1	3	yes	—
26	C₃³	#733	1	6	yes	—
27	C₃³	C₃×H(3,𝔽₃)	1	1	yes	characteristic
28	C₃×C₉	—	3	2	no	—
29	C₃×C₉	—	3	1	no	—
30	C₃×C₉	—	3	2	no	—
31	C₃×C₉	—	3	1	no	—
32	C₃×C₉	—	3	4	no	—
33	C₃×C₉	—	3	2	no	—
34	C₃×C₉	—	9	9	no	—
35	C₃×C₉	—	9	3	no	—
36	C₃×C₉	—	9	6	no	—
37	C₃×C₉	—	9	3	no	—
38	C₃×C₉	—	9	9	no	—
39	C₃×C₉	—	27	9	no	—
40	C₃²	—	3	1	no	—
41	C₃²	—	3	3	no	—
42	C₃²	—	3	2	no	—
43	C₃²	—	3	6	no	—
44	C₃²	—	9	3	no	—
45	C₃²	—	9	6	no	—
46	C₃²	#6861	1	9	yes	—
47	C₃²	C₃×#731	1	1	yes	characteristic
48	C₃²	C₃×#732	1	1	yes	characteristic
49	C₃²	C₃×#733	1	2	yes	—
50	C₉	—	9	2	no	—
51	C₉	—	9	1	no	—
52	C₉	—	27	3	no	—
53	C₉	—	27	9	no	—
54	C₃	—	3	1	no	—
55	C₃	—	3	9	no	—
56	C₃	—	3	2	no	—
57	C₃	C₃×#6861	1	1	yes	characteristic
58	C₃	#10624839	1	1	yes	characteristic
59	C₃	#10624847	1	2	yes	—

	subgroup	G/H
center, socle	C₃²	C₃×#732
commutator, Frattini, cosocle	C₃²×C₉	C₃³
prime radical	C₃⁴	H(3,𝔽₃)
LCS	G ▷ C₃²×C₉ ▷ C₃³ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃² ◁ C₃⁴ ◁ C₃³×C₉ ◁ G
LECS	G ▷ C₃²×C₉ ▷ C₃³ ▷ C₃ ▷ C₁

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

N	H ≅ G/N	type
3. #10624494	C₃	semidirect

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