Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
294 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 86 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×C4×#732 | C2 | semidirect |
| 3. C2×#66325 | C2 | semidirect |
| 4. C4×#4178 | C2 | direct (N × H) |
| 5. C2×C4×#272 | C3 | semidirect |
| 8. C2×#4178 | C4 | direct (N × H) |
| 10. C4×#732 | C22 | semidirect |
| 11. #66325 | C22 | semidirect |
| 16. C2×C3×C4×C9 | D3 | semidirect |
| 18. C4×#272 | C2×C3 | semidirect |
| 21. C2×#732 | C2×C4 | semidirect |
| 23. #4178 | C2×C4 | direct (N × H) |
| 30. C2×#272 | C3×C4 | semidirect |
| 36. C3×C4×C9 | C2×D3 | semidirect |
| 39. #732 | C22×C4 | semidirect |
| 57. C2×C3×C9 | C4×D3 | semidirect |
| 59. #272 | C2×C3×C4 | semidirect |
| 83. C3×C9 | C2×C4×D3 | semidirect |
| 133. C2×C4 | #4178 | direct (N × H) |
| 149. C4 | C2×#4178 | direct (N × H) |
| 155. C2 | C4×#4178 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4178 | 2 |
| C2×C4×#732 | 2 |
| C2×#66325 | 2 |
| C4×#4178 | 2 |
| C2×C4×#272 | 3 |
| C2×C4×D3×C9 | 3 |