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. C4×C9×C3⋊D3 | C2 | semidirect |
| 3. C32×D36 | C2 | semidirect |
| 4. #10619877 | C2 | semidirect |
| 5. D9×C3⋊Dic3 | C2 | semidirect |
| 21. C3×D36 | D3 | semidirect |
| 42. C32×C9 | #41 | semidirect |
| 46. C4×C3⋊D3 | D9 | semidirect |
| 56. D36 | C3⋊D3 | semidirect |
| 90. C3×C9 | #237 | semidirect |
| 127. C32 | #3697 | semidirect |
| 130. C9 | #3830 | semidirect |
| 149. C3 | #88641 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10619985 | 2 |
| C4×C9×C3⋊D3 | 2 |
| C32×D36 | 2 |
| #10619877 | 2 |
| D9×C3⋊Dic3 | 2 |
| #89014 | 3 |
| #88641 | 3 |