Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
614 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 614 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×D9×C3⋊D3 | C2 | semidirect |
| 2. C4⋊(C3⋊(C3⋊D9)) | C2 | semidirect |
| 3. C9×C4⋊(C3⋊D3) | C2 | semidirect |
| 4. C32×C4×D9 | C2 | semidirect |
| 5. #10619878 | C2 | semidirect |
| 8. C2×C3⋊(C3⋊D9) | C22 | semidirect |
| 9. C2×C9×C3⋊D3 | C22 | semidirect |
| 12. C32×C4×C9 | C22 | semidirect |
| 13. C32×Dic9 | C22 | semidirect |
| 23. C3×C4×D9 | D3 | semidirect |
| 28. C32×D9 | D4 | semidirect |
| 44. C3×C4×C9 | C2×D3 | semidirect |
| 45. C3×Dic9 | C2×D3 | semidirect |
| 46. C32×C9 | C2×D4 | semidirect |
| 54. C4⋊(C3⋊D3) | D9 | direct (N × H) |
| 63. C4×D9 | C3⋊D3 | semidirect |
| 73. C3×D9 | D12 | semidirect |
| 81. C2×C3⋊D3 | C2×D9 | semidirect |
| 87. C32×C4 | C2×D9 | semidirect |
| 96. C4×C9 | C2×C3⋊D3 | semidirect |
| 97. Dic9 | C2×C3⋊D3 | semidirect |
| 100. C3×C9 | C2×D12 | semidirect |
| 127. D9 | C4⋊(C3⋊D3) | direct (N × H) |
| 140. C3×C4 | D3×D9 | semidirect |
| 144. C32 | D4×D9 | semidirect |
| 147. C9 | C2×C4⋊(C3⋊D3) | semidirect |
| 168. C4 | D9×C3⋊D3 | semidirect |
| 170. C3 | D9×D12 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D9×C3⋊D3 | 2 |
| C4⋊(C3⋊(C3⋊D9)) | 2 |
| C9×C4⋊(C3⋊D3) | 2 |
| C32×C4×D9 | 2 |
| #10619878 | 2 |
| D3×C4⋊(C3⋊D3) | 3 |
| D9×D12 | 3 |