Subgroups — C₃²×#6898 #14555296

Order 2187.

3932 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#6898	C₃	1	108	yes	maximal, direct product factor
2	C₃²×C₉⋊C₉	C₃	1	8	yes	maximal, complemented
3	C₃²×C₃²⋊C₉	C₃	1	4	yes	maximal
4	C₃²×C₉²	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃⁵	C₃²	1	1	yes	characteristic
6	C₃³×C₉	C₃²	1	4	yes	—
7	C₃³×C₉	C₃²	1	8	yes	—
8	#6898	C₃²	1	729	yes	direct product factor
9	C₃×C₉⋊C₉	C₃²	1	288	yes	complemented
10	C₃×C₃²⋊C₉	C₃²	1	144	yes	—
11	C₃×C₉²	C₃²	1	36	yes	complemented
12	C₃⁴	—	3	36	no	—
13	C₃⁴	C₃³	1	12	yes	—
14	C₃⁴	C₃³	1	1	yes	characteristic
15	C₃²×C₉	—	3	36	no	—
16	C₃²×C₉	—	3	72	no	—
17	C₃²×C₉	C₃³	1	48	yes	—
18	C₃²×C₉	C₃³	1	96	yes	—
19	C₉⋊C₉	C₃³	1	648	yes	complemented
20	C₃²⋊C₉	C₃³	1	324	yes	—
21	C₉²	C₃³	1	81	yes	complemented
22	C₃³	—	3	144	no	—
23	C₃³	—	9	81	no	—
24	C₃³	#737	1	36	yes	—
25	C₃³	C₃⁴	1	9	yes	—
26	C₃³	C₃⁴	1	4	yes	—
27	C₃×C₉	—	3	144	no	—
28	C₃×C₉	—	3	288	no	—
29	C₃×C₉	C₃⁴	1	36	yes	—
30	C₃×C₉	C₃⁴	1	72	yes	—
31	C₃²	—	3	36	no	—
32	C₃²	—	9	108	no	—
33	C₃²	#6898	1	81	yes	direct product factor
34	C₃²	C₃×#737	1	48	yes	—
35	C₃²	C₃⁵	1	1	yes	characteristic
36	C₉	—	3	36	no	—
37	C₉	—	3	72	no	—
38	C₃	—	9	9	no	—
39	C₃	C₃×#6898	1	36	yes	direct product factor
40	C₃	C₃²×#737	1	4	yes	—

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

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

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