Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
488 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 89 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. C4⋊(C3⋊(C3⋊D9)) | C2 | semidirect |
| 2. C4×C9×C3⋊D3 | C2 | semidirect |
| 3. C32×Dic18 | C2 | semidirect |
| 4. #10619878 | C2 | semidirect |
| 5. #10619870 | C2 | semidirect |
| 21. C3×Dic18 | D3 | semidirect |
| 42. C32×C9 | #41 | semidirect |
| 49. C4×C3⋊D3 | D9 | semidirect |
| 59. Dic18 | C3⋊D3 | semidirect |
| 91. C3×C9 | #239 | semidirect |
| 130. C32 | #3697 | semidirect |
| 133. C9 | #3832 | semidirect |
| 153. C3 | #88642 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊(C3⋊(C3⋊D9)) | 2 |
| C4×C9×C3⋊D3 | 2 |
| C32×Dic18 | 2 |
| #10619878 | 2 |
| #10619870 | 2 |
| #89018 | 3 |
| #88642 | 3 |