Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
490 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 104 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. C3×C4×C3⋊D9 | C2 | semidirect |
| 3. C3×C9×D12 | C2 | semidirect |
| 4. #10619879 | C2 | semidirect |
| 5. D3×C3⋊Dic9 | C2 | semidirect |
| 22. C4×C3⋊D9 | D3 | semidirect |
| 27. C9×D12 | D3 | semidirect |
| 57. C32×C9 | #41 | semidirect |
| 67. C3×D12 | D9 | semidirect |
| 124. C3×C9 | #235 | semidirect |
| 125. C3×C9 | #237 | semidirect |
| 134. D12 | C3⋊D9 | semidirect |
| 180. C32 | #3699 | semidirect |
| 184. C9 | #3795 | semidirect |
| 208. C3 | #88638 | semidirect |
| 209. C3 | #88742 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10619985 | 2 |
| C3×C4×C3⋊D9 | 2 |
| C3×C9×D12 | 2 |
| #10619879 | 2 |
| D3×C3⋊Dic9 | 2 |
| #89014 | 3 |
| #88742 | 3 |
| #88638 | 3 |