Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
620 conjugacy classes of subgroups; only the 256 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 256 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. #17987456 | C3 | semidirect |
| 2. #17987455 | C3 | semidirect |
| 3. #17987454 | C3 | semidirect |
| 4. #17987453 | C3 | semidirect |
| 5. #17987449 | C3 | semidirect |
| 6. #17987448 | C3 | semidirect |
| 7. #17987441 | C3 | semidirect |
| 8. #17987440 | C3 | semidirect |
| 9. #17987435 | C3 | semidirect |
| 13. C9×#10587025 | C3 | semidirect |
| 15. C9×C19×3−1+2 | C3 | semidirect |
| 21. #13095307 | C32 | semidirect |
| 22. #13095306 | C32 | semidirect |
| 23. #13095305 | C32 | semidirect |
| 24. #13095305 | C32 | semidirect |
| 25. #13095305 | C32 | semidirect |
| 26. #13095305 | C32 | semidirect |
| 27. #13095305 | C32 | semidirect |
| 28. #13095305 | C32 | semidirect |
| 29. #13095305 | C32 | semidirect |
| 30. #13095305 | C32 | semidirect |
| 31. #13095305 | C32 | semidirect |
| 47. C9×#4294 | C32 | semidirect |
| 50. C19×C9⋊C9 | C32 | semidirect |
| 53. C92×C19 | C32 | semidirect |
| 93. C9×3−1+2 | C19⋊C3 | semidirect |
| 142. C9⋊C9 | C3×C19⋊C3 | semidirect |
| 161. C92 | C3×C19⋊C3 | semidirect |
| 195. C19 | #10624889 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987456 | 3 |
| #17987455 | 3 |
| #17987454 | 3 |
| #17987453 | 3 |
| #17987449 | 3 |
| #17987448 | 3 |
| #17987441 | 3 |
| #17987440 | 3 |
| #17987435 | 3 |
| #17987420 | 3 |
| #17987419 | 3 |
| #17987418 | 3 |
| C9×#10587025 | 3 |
| C3×#13095303 | 3 |
| C9×C19×3−1+2 | 3 |
| #10624889 | 19 |