Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
545 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 545 conjugacy classes of subgroups — too many to draw. Only its 203 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×#66328 | C2 | direct (N × H) |
| 5. C22×C32⋊C9 | C4 | semidirect |
| 7. #66328 | C22 | direct (N × H) |
| 12. C2×C32⋊C9 | C2×C4 | semidirect |
| 21. C22×C3×C9 | Dic3 | semidirect |
| 24. C32⋊C9 | C22×C4 | semidirect |
| 36. C2×C3×C9 | C2×Dic3 | semidirect |
| 45. C22×C32 | Dic9 | semidirect |
| 56. C3×C9 | C22×Dic3 | semidirect |
| 68. C2×C32 | C2×Dic9 | semidirect |
| 88. C32 | C22×Dic9 | semidirect |
| 101. C22 | #66328 | direct (N × H) |
| 108. C2 | C2×#66328 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C32⋊C9 | 2 |
| C2×#66328 | 2 |
| C22×C3×C3⋊Dic3 | 3 |
| C22×C3×Dic9 | 3 |