Subgroups — C₃²×#66851 #15691689

Order 3159.

576 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#66851	C₃	1	36	yes	maximal, direct product factor
2	C₃²×C₁₃⋊C₉	C₃	1	3	yes	maximal, complemented
3	C₃⁴×C₁₃	C₃	1	1	yes	maximal, characteristic
4	C₃³×C₁₃	—	3	9	no	—
5	C₃³×C₁₃	C₃²	1	12	yes	—
6	C₃³×C₁₃	C₃²	1	1	yes	characteristic
7	#66851	C₃²	1	81	yes	direct product factor
8	C₃×C₁₃⋊C₉	C₃²	1	36	yes	complemented
9	C₃²×3₋¹⁺²	—	13	1	no	maximal, Sylow
10	C₃²×C₁₃	—	3	36	no	—
11	C₃²×C₁₃	3₋¹⁺²	1	9	yes	complemented
12	C₃²×C₁₃	C₃³	1	9	yes	—
13	C₃²×C₁₃	C₃³	1	4	yes	—
14	C₁₃⋊C₉	C₃³	1	27	yes	complemented
15	C₃⁴	C₁₃⋊C₃	1	1	yes	characteristic
16	C₃×3₋¹⁺²	—	13	36	no	—
17	C₃²×C₉	—	13	3	no	—
18	C₃×C₁₃	—	3	9	no	—
19	C₃×C₁₃	C₃×3₋¹⁺²	1	12	yes	complemented
20	C₃×C₁₃	C₃⁴	1	1	yes	characteristic
21	C₃³	—	3	9	no	—
22	C₃³	C₃×C₁₃⋊C₃	1	12	yes	—
23	C₃³	C₃×C₁₃⋊C₃	1	1	yes	characteristic
24	3₋¹⁺²	—	13	81	no	—
25	C₃×C₉	—	13	36	no	—
26	C₁₃	C₃²×3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
27	C₃²	—	3	36	no	—
28	C₃²	#66851	1	9	yes	direct product factor
29	C₃²	C₃²×C₁₃⋊C₃	1	9	yes	—
30	C₃²	C₃²×C₁₃⋊C₃	1	4	yes	—
31	C₉	—	13	27	no	—
32	C₃	—	3	9	no	—
33	C₃	C₃×#66851	1	12	yes	direct product factor
34	C₃	C₃³×C₁₃⋊C₃	1	1	yes	characteristic

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.