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. #17987547 | C3 | semidirect |
| 2. C3×#13095333 | C3 | semidirect |
| 3. #17987525 | C3 | semidirect |
| 4. #17987524 | C3 | semidirect |
| 5. #17987519 | C3 | semidirect |
| 6. #17987504 | C3 | semidirect |
| 7. #17987498 | C3 | semidirect |
| 8. C3×#13095316 | C3 | semidirect |
| 9. C19×#6911 | C3 | semidirect |
| 12. #13095331 | C32 | semidirect |
| 16. C3×#10587022 | C32 | semidirect |
| 17. C3×#10587023 | C32 | semidirect |
| 20. C3×C9×C19⋊C3 | C32 | semidirect |
| 21. #13095322 | C32 | semidirect |
| 22. #13095316 | C32 | semidirect |
| 23. #13095316 | C32 | semidirect |
| 24. #13095316 | C32 | semidirect |
| 25. #13095313 | C32 | semidirect |
| 58. #6911 | C19⋊C3 | semidirect |
| 122. C19 | #10624935 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987547 | 3 |
| C3×#13095333 | 3 |
| #17987525 | 3 |
| #17987524 | 3 |
| #17987519 | 3 |
| #17987504 | 3 |
| #17987498 | 3 |
| C3×#13095316 | 3 |
| C19×#6911 | 3 |
| #10624935 | 19 |