Finite Group DatabasebetaFinite Group Databasebeta← C3⋊((C3⋊D3)⋊(C22⋊C9)) #14518262
Order 1944.
572 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C32⋊(C22⋊C9) | C2 | semidirect |
| 10. C32×C22⋊C9 | D3 | semidirect |
| 12. C32⋊(C22⋊C9) | D3 | semidirect |
| 14. C22×C3⋊(C3⋊D3) | C9 | semidirect |
| 29. C22×C33 | C2×C9 | semidirect |
| 44. C3×C22⋊C9 | C3⋊D3 | semidirect |
| 65. C3⋊(C3⋊D3) | C22⋊C9 | semidirect |
| 83. C22×C32 | D3×C9 | semidirect |
| 105. C33 | C2×C22⋊C9 | semidirect |
| 148. C22×C3 | (C3⋊D3)⋊C9 | semidirect |
| 166. C32 | D3×C22⋊C9 | semidirect |
| 190. C22 | C3⋊((C3⋊D3)⋊C9) | semidirect |
| 195. C3 | (C3⋊D3)⋊(C22⋊C9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C32⋊(C22⋊C9) | 2 |
| C22×C3×C3⋊(C3⋊D3) | 3 |
| C3⋊D3×C22⋊C9 | 3 |
| (C3⋊D3)⋊(C22⋊C9) | 3 |
| C3⋊((C3⋊D3)⋊C9) | 4 |