Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
490 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 230 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. C32×Q8×C9 | C2 | semidirect |
| 2. C3×C9×D12 | C2 | semidirect |
| 3. C3×C4×D3×C9 | C2 | semidirect |
| 6. C9×#239 | C3 | direct (N × H) |
| 15. C3×Q8×C9 | D3 | semidirect |
| 16. C3×Q8×C9 | C2×C3 | semidirect |
| 19. C9×D12 | C2×C3 | semidirect |
| 20. C4×D3×C9 | C2×C3 | semidirect |
| 24. C3×#239 | C9 | direct (N × H) |
| 38. C32×C9 | #41 | semidirect |
| 41. C32×Q8 | C2×C9 | semidirect |
| 46. C3×D12 | C2×C9 | semidirect |
| 48. C3×C4×D3 | C2×C9 | semidirect |
| 51. Q8×C9 | C3×D3 | semidirect |
| 64. #239 | C3×C9 | direct (N × H) |
| 83. C3×C9 | #239 | direct (N × H) |
| 84. C3×C9 | C3×#41 | semidirect |
| 87. C3×Q8 | D3×C9 | semidirect |
| 88. C3×Q8 | C2×C3×C9 | semidirect |
| 94. D12 | C2×C3×C9 | semidirect |
| 95. C4×D3 | C2×C3×C9 | semidirect |
| 121. C32 | C9×#41 | semidirect |
| 125. C9 | C3×#239 | direct (N × H) |
| 126. Q8 | C3×D3×C9 | semidirect |
| 142. C3 | C9×#239 | direct (N × H) |
| 143. C3 | C3×C9×#41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×Q8×C9 | 2 |
| C3×C9×D12 | 2 |
| C3×C4×D3×C9 | 2 |
| C32×#239 | 3 |
| C3×C9×#41 | 3 |
| C9×#239 | 3 |