Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
438 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
| 3. C32×Dic18 | C2 | semidirect |
| 5. #10619867 | C2 | semidirect |
| 21. C3×Dic18 | D3 | semidirect |
| 25. C9×C3⋊D3 | Q8 | semidirect |
| 41. C32×C9 | C2×Q8 | semidirect |
| 58. Dic18 | C3⋊D3 | direct (N × H) |
| 87. C3×C9 | D3×Q8 | semidirect |
| 102. C3⋊D3 | Dic18 | direct (N × H) |
| 121. C32 | C2×Dic18 | semidirect |
| 124. C9 | Q8×C3⋊D3 | semidirect |
| 141. C3 | D3×Dic18 | 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×Dic18 | 2 |
| C3⋊D3×Dic9 | 2 |
| #10619867 | 2 |
| C3⋊D3×Dic6 | 3 |
| D3×Dic18 | 3 |