Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
500 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 2. C3×#6226 | C2 | semidirect |
| 3. C3×C9×Dic6 | C2 | semidirect |
| 5. #10619868 | C2 | semidirect |
| 26. #6226 | D3 | semidirect |
| 27. C9×Dic6 | D3 | semidirect |
| 32. C3⋊(C3⋊D9) | Q8 | semidirect |
| 58. C32×C9 | C2×Q8 | semidirect |
| 70. C3×Dic6 | D9 | semidirect |
| 127. C3×C9 | D3×Q8 | semidirect |
| 128. C3×C9 | D3×Q8 | semidirect |
| 145. Dic6 | C3⋊D9 | semidirect |
| 184. C32 | Q8×D9 | semidirect |
| 188. C9 | #3797 | semidirect |
| 211. C3 | (C3⋊D9)⋊Q8 | semidirect |
| 212. C3 | Q8×C3⋊D9 | 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 |
| C3×#6226 | 2 |
| C3×C9×Dic6 | 2 |
| #10619872 | 2 |
| #10619868 | 2 |
| #89019 | 3 |
| Q8×C3⋊D9 | 3 |
| (C3⋊D9)⋊Q8 | 3 |