Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
240 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 100 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. C22×D3×C27 | C2 | semidirect |
| 2. C3×D4×C27 | C2 | semidirect |
| 3. #67×C27 | C2 | semidirect |
| 4. D12×C27 | C2 | semidirect |
| 5. C4×D3×C27 | C2 | semidirect |
| 8. C22×C3×C27 | C22 | semidirect |
| 11. C2×D3×C27 | C22 | semidirect |
| 12. C3×C4×C27 | C22 | semidirect |
| 13. Dic3×C27 | C22 | semidirect |
| 23. D4×C27 | D3 | direct (N × H) |
| 28. D3×C27 | D4 | direct (N × H) |
| 41. C22×C27 | C2×D3 | semidirect |
| 44. C4×C27 | C2×D3 | semidirect |
| 45. C3×C27 | C2×D4 | semidirect |
| 68. D3×D4 | C27 | direct (N × H) |
| 85. C27 | D3×D4 | direct (N × H) |
| 87. C22×D3 | C2×C27 | semidirect |
| 91. C3×D4 | C2×C27 | semidirect |
| 94. #67 | C2×C27 | semidirect |
| 95. D12 | C2×C27 | semidirect |
| 96. C4×D3 | C2×C27 | semidirect |
| 112. C22×C3 | C22×C27 | semidirect |
| 116. C2×D3 | C22×C27 | semidirect |
| 119. C3×C4 | C22×C27 | semidirect |
| 121. Dic3 | C22×C27 | semidirect |
| 128. D4 | D3×C27 | direct (N × H) |
| 139. D3 | D4×C27 | direct (N × H) |
| 143. C22 | C2×D3×C27 | semidirect |
| 145. C4 | C2×D3×C27 | semidirect |
| 147. C3 | C2×D4×C27 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×C27 | 2 |
| C3×D4×C27 | 2 |
| #67×C27 | 2 |
| D12×C27 | 2 |
| C4×D3×C27 | 2 |
| D3×D4×C9 | 3 |
| C2×D4×C27 | 3 |