Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
270 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 6. C9×#216 | C3 | direct (N × H) |
| 23. C3×#216 | C9 | direct (N × H) |
| 39. C32×C9 | Q16 | semidirect |
| 62. #216 | C3×C9 | direct (N × H) |
| 84. C3×C9 | #216 | direct (N × H) |
| 85. C3×C9 | C3×Q16 | semidirect |
| 120. C32 | C9×Q16 | semidirect |
| 124. C9 | C3×#216 | direct (N × H) |
| 138. C3 | C9×#216 | direct (N × H) |
| 139. C3 | C3×C9×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×Q8×C9 | 2 |
| C3×C9×Dic6 | 2 |
| C3×C9×C3⋊C8 | 2 |
| C32×#216 | 3 |
| C3×C9×Q16 | 3 |
| C9×#216 | 3 |