Subgroups — #10624913

Order 729.

298 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6898	C₃	1	18	yes	maximal, complemented
2	#6896	C₃	1	18	yes	maximal, complemented
3	#6891	C₃	1	4	yes	maximal
4	C₃⁴	C₃²	1	1	yes	characteristic
5	C₃×3₋¹⁺²	C₃²	1	12	yes	—
6	C₉⋊C₉	C₃²	1	72	yes	complemented
7	C₃²⋊C₉	C₃²	1	12	yes	—
8	C₃²⋊C₉	C₃²	1	24	yes	—
9	C₉²	C₃²	1	9	yes	complemented
10	C₃³	—	9	4	no	—
11	C₃³	C₃³	1	2	yes	—
12	C₃³	C₃³	1	2	yes	—
13	3₋¹⁺²	—	9	12	no	—
14	C₃×C₉	C₃³	1	36	yes	—
15	C₃²	—	3	4	no	—
16	C₃²	—	3	8	no	—
17	C₃²	—	3	4	no	—
18	C₃²	—	9	9	no	—
19	C₃²	C₃⁴	1	1	yes	characteristic
20	C₉	—	3	36	no	—
21	C₃	—	9	2	no	—
22	C₃	—	9	2	no	—
23	C₃	3₋¹⁺⁴	1	4	yes	—

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