Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
312 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
| 4. #10619895 | C2 | semidirect |
| 15. #6226 | D3 | semidirect |
| 23. C9×C3⋊D3 | Q8 | semidirect |
| 42. C32×C9 | C2×Q8 | semidirect |
| 95. C3×C9 | D3×Q8 | semidirect |
| 112. C3⋊D3 | Dic18 | semidirect |
| 138. C32 | C2×Dic18 | semidirect |
| 142. C9 | #3797 | semidirect |
| 162. C3 | D3×Dic18 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C9×C3⋊D3 | 2 |
| C3×#6226 | 2 |
| #10619898 | 2 |
| #10619895 | 2 |
| #89040 | 3 |
| D3×Dic18 | 3 |