Subgroups — C₃²×#11719689 #21419429

Order 7533.

576 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#11719689	C₃	1	36	yes	maximal, direct product factor
2	C₃²×C₃₁⋊C₉	C₃	1	3	yes	maximal, complemented
3	C₃⁴×C₃₁	C₃	1	1	yes	maximal, characteristic
4	C₃³×C₃₁	—	3	9	no	—
5	C₃³×C₃₁	C₃²	1	12	yes	—
6	C₃³×C₃₁	C₃²	1	1	yes	characteristic
7	#11719689	C₃²	1	81	yes	direct product factor
8	C₃×C₃₁⋊C₉	C₃²	1	36	yes	complemented
9	C₃²×C₃₁	—	3	36	no	—
10	C₃²×C₃₁	3₋¹⁺²	1	9	yes	complemented
11	C₃²×C₃₁	C₃³	1	9	yes	—
12	C₃²×C₃₁	C₃³	1	4	yes	—
13	C₃₁⋊C₉	C₃³	1	27	yes	complemented
14	C₃²×3₋¹⁺²	—	31	1	no	maximal, Sylow
15	C₃×C₃₁	—	3	9	no	—
16	C₃×C₃₁	C₃×3₋¹⁺²	1	12	yes	complemented
17	C₃×C₃₁	C₃⁴	1	1	yes	characteristic
18	C₃⁴	C₃₁⋊C₃	1	1	yes	characteristic
19	C₃×3₋¹⁺²	—	31	36	no	—
20	C₃²×C₉	—	31	3	no	—
21	C₃₁	C₃²×3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
22	C₃³	—	3	9	no	—
23	C₃³	C₃×C₃₁⋊C₃	1	12	yes	—
24	C₃³	C₃×C₃₁⋊C₃	1	1	yes	characteristic
25	3₋¹⁺²	—	31	81	no	—
26	C₃×C₉	—	31	36	no	—
27	C₃²	—	3	36	no	—
28	C₃²	#11719689	1	9	yes	direct product factor
29	C₃²	C₃²×C₃₁⋊C₃	1	9	yes	—
30	C₃²	C₃²×C₃₁⋊C₃	1	4	yes	—
31	C₉	—	31	27	no	—
32	C₃	—	3	9	no	—
33	C₃	C₃×#11719689	1	12	yes	direct product factor
34	C₃	C₃³×C₃₁⋊C₃	1	1	yes	characteristic

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