Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
318 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 1. C23×#732 | C2 | semidirect |
| 2. C22×#4178 | C2 | semidirect |
| 3. #10619649 | C2 | direct (N × H) |
| 4. C2×#66325 | C2 | semidirect |
| 5. C2×#6235 | C3 | semidirect |
| 9. C22×#732 | C22 | semidirect |
| 11. C2×#4178 | C22 | semidirect |
| 12. #66325 | C22 | semidirect |
| 15. C23×C3×C9 | D3 | semidirect |
| 16. C22×#272 | C2×C3 | semidirect |
| 18. #6235 | C2×C3 | semidirect |
| 19. C2×#1084 | C2×C3 | semidirect |
| 23. C2×#732 | D4 | semidirect |
| 37. C22×C3×C9 | C2×D3 | semidirect |
| 39. C2×#272 | C22×C3 | semidirect |
| 42. #1084 | C22×C3 | semidirect |
| 44. #732 | C2×D4 | semidirect |
| 65. C2×C3×C9 | #67 | semidirect |
| 95. C3×C9 | C2×#67 | semidirect |
| 151. C23 | #4178 | semidirect |
| 173. C22 | C2×#4178 | semidirect |
| 181. C2 | #10619649 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#732 | 2 |
| C22×#4178 | 2 |
| #10619649 | 2 |
| C2×#66325 | 2 |
| C2×#6235 | 3 |
| C2×C9×#67 | 3 |