Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
302 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 118 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. C2×#66323 | C2 | direct (N × H) |
| 5. C22×#731 | C4 | semidirect |
| 7. #66323 | C22 | direct (N × H) |
| 13. C2×#731 | C2×C4 | semidirect |
| 22. C22×C3×C9 | Dic3 | semidirect |
| 26. #731 | C22×C4 | semidirect |
| 38. C2×C3×C9 | C2×Dic3 | semidirect |
| 56. C3×C9 | C22×Dic3 | semidirect |
| 93. C22 | #66323 | direct (N × H) |
| 99. C2 | C2×#66323 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#731 | 2 |
| C2×#66323 | 2 |
| C22×#1084 | 3 |
| C22×C9×Dic3 | 3 |