Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
198 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 48 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 |
|---|---|---|
| 3. C22×C3×Dic9 | C3 | semidirect |
| 4. Dic9⋊A4 | C3 | direct (N × H) |
| 5. C3×C9⋊A4 | C4 | semidirect |
| 18. C22×Dic9 | C32 | semidirect |
| 23. C22×C3×C9 | C3×C4 | semidirect |
| 26. C9⋊A4 | C3×C4 | semidirect |
| 29. C3×Dic9 | A4 | semidirect |
| 67. C22×C9 | C32×C4 | semidirect |
| 70. Dic9 | C3×A4 | semidirect |
| 75. C3×C9 | C4×A4 | semidirect |
| 105. C22×C3 | 3−1+2⋊C4 | semidirect |
| 119. C9 | C3×C4×A4 | semidirect |
| 135. C22 | C3×3−1+2⋊C4 | semidirect |
| 140. C3 | Dic9⋊A4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C9⋊A4 | 2 |
| C3×Dic3×A4 | 3 |
| C22×C3×Dic9 | 3 |
| Dic9⋊A4 | 3 |
| C3×3−1+2⋊C4 | 4 |