Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
948 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 948 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. #17987546 | C3 | semidirect |
| 2. C3×#13095333 | C3 | semidirect |
| 3. #17987530 | C3 | semidirect |
| 4. #17987529 | C3 | semidirect |
| 5. #17987519 | C3 | semidirect |
| 6. #17987515 | C3 | semidirect |
| 7. #17987506 | C3 | semidirect |
| 8. #17987501 | C3 | semidirect |
| 9. C3×#13095318 | C3 | semidirect |
| 10. C19×#6912 | C3 | semidirect |
| 13. #13095333 | C32 | semidirect |
| 17. C3×#10587022 | C32 | semidirect |
| 18. C3×#10587023 | C32 | semidirect |
| 23. C3×C9×C19⋊C3 | C32 | semidirect |
| 24. #13095322 | C32 | semidirect |
| 26. #13095318 | C32 | semidirect |
| 27. #13095318 | C32 | semidirect |
| 28. #13095318 | C32 | semidirect |
| 29. #13095315 | C32 | semidirect |
| 32. C19×#733 | C32 | semidirect |
| 68. #6912 | C19⋊C3 | semidirect |
| 103. #733 | C3×C19⋊C3 | semidirect |
| 143. C19 | #10624935 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987546 | 3 |
| C3×#13095333 | 3 |
| #17987530 | 3 |
| #17987529 | 3 |
| #17987519 | 3 |
| #17987515 | 3 |
| #17987506 | 3 |
| #17987501 | 3 |
| C3×#13095318 | 3 |
| C19×#6912 | 3 |
| #10624935 | 19 |