Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
960 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 960 conjugacy classes of subgroups — too many to draw. Only its 268 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. C3×#13095333 | C3 | semidirect |
| 2. C3×#13095333 | C3 | semidirect |
| 3. #17987530 | C3 | semidirect |
| 4. #17987529 | C3 | semidirect |
| 5. #17987519 | C3 | semidirect |
| 6. #17987515 | C3 | semidirect |
| 7. #17987511 | C3 | semidirect |
| 8. #17987506 | C3 | semidirect |
| 9. #17987501 | C3 | semidirect |
| 10. C19×#6912 | C3 | semidirect |
| 20. #13095333 | C32 | semidirect |
| 21. #13095333 | C32 | semidirect |
| 22. #13095333 | C32 | semidirect |
| 26. C3×#10587022 | C32 | semidirect |
| 28. C3×#10587023 | C32 | semidirect |
| 33. C3×C9×C19⋊C3 | C32 | semidirect |
| 34. #13095322 | C32 | semidirect |
| 36. #13095318 | C32 | semidirect |
| 37. #13095315 | C32 | semidirect |
| 40. C19×#733 | C32 | semidirect |
| 86. #6912 | C19⋊C3 | semidirect |
| 133. #733 | C3×C19⋊C3 | semidirect |
| 181. C19 | #10624929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#13095333 | 3 |
| #17987530 | 3 |
| #17987529 | 3 |
| #17987519 | 3 |
| #17987515 | 3 |
| #17987511 | 3 |
| #17987506 | 3 |
| #17987501 | 3 |
| C19×#6912 | 3 |
| #10624929 | 19 |