Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
268 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 82 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. C9×#10587025 | C3 | semidirect |
| 4. C3×#13095305 | C3 | semidirect |
| 5. 3−1+2⋊#4294 | C3 | semidirect |
| 6. 3−1+2⋊#4294 | C3 | semidirect |
| 7. #17987345 | C3 | semidirect |
| 8. #17987345 | C3 | semidirect |
| 11. #17987336 | C3 | semidirect |
| 12. #17987336 | C3 | semidirect |
| 13. C9×C19×3−1+2 | C3 | semidirect |
| 20. #13095318 | C9 | semidirect |
| 44. C19×3−1+2 | C3×C9 | semidirect |
| 55. #10587025 | C3×C9 | semidirect |
| 67. C3×#4294 | C3×C9 | semidirect |
| 71. C9×3−1+2 | C19⋊C3 | semidirect |
| 144. 3−1+2 | C9×C19⋊C3 | semidirect |
| 167. C19 | #731⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#13095318 | 3 |
| C9×#10587025 | 3 |
| C9×C32⋊(C19⋊C3) | 3 |
| C3×#13095305 | 3 |
| 3−1+2⋊#4294 | 3 |
| #17987345 | 3 |
| #17987342 | 3 |
| #17987336 | 3 |
| C9×C19×3−1+2 | 3 |
| #731⋊C9 | 19 |