Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
258 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 17. #3756 | C9 | direct (N × H) |
| 28. C32×C9 | Q16 | semidirect |
| 60. C3×C9 | #216 | semidirect |
| 83. C32 | C9×Q16 | semidirect |
| 86. C9 | #3756 | direct (N × H) |
| 97. C3 | C9×#216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×Q8×C9 | 2 |
| C9×#634 | 2 |
| C9×C3⋊(C3⋊C8) | 2 |
| C3×#3756 | 3 |
| C9×#216 | 3 |