Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
244 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 65 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. C32×Dic18 | C2 | semidirect |
| 3. C3⋊(C3⋊(C9⋊C8)) | C2 | semidirect |
| 13. C3×Dic18 | D3 | semidirect |
| 28. C32×C9 | SD16 | semidirect |
| 37. Dic18 | C3⋊D3 | semidirect |
| 60. C3×C9 | #215 | semidirect |
| 85. C32 | #3672 | semidirect |
| 88. C9 | #3755 | semidirect |
| 101. C3 | #88423 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×C4⋊(C3⋊D3) | 2 |
| C32×Dic18 | 2 |
| C3⋊(C3⋊(C9⋊C8)) | 2 |
| #88793 | 3 |
| #88423 | 3 |