Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
456 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 456 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. #10619985 | C2 | semidirect |
| 2. C9×C4⋊(C3⋊D3) | C2 | semidirect |
| 3. C32×C4×D9 | C2 | semidirect |
| 4. #10619877 | C2 | semidirect |
| 5. C3⋊D3×Dic9 | C2 | semidirect |
| 21. C3×C4×D9 | D3 | semidirect |
| 42. C32×C9 | #41 | semidirect |
| 45. C4⋊(C3⋊D3) | D9 | semidirect |
| 57. C4×D9 | C3⋊D3 | semidirect |
| 90. C3×C9 | #235 | semidirect |
| 127. C32 | #3699 | semidirect |
| 130. C9 | #3828 | semidirect |
| 149. C3 | #88638 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10619985 | 2 |
| C9×C4⋊(C3⋊D3) | 2 |
| C32×C4×D9 | 2 |
| #10619877 | 2 |
| C3⋊D3×Dic9 | 2 |
| #89021 | 3 |
| #88638 | 3 |