Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
198 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 49 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. #17987441 | C3 | semidirect |
| 2. #17987435 | C3 | semidirect |
| 3. #17987432 | C3 | semidirect |
| 4. #17987427 | C3 | semidirect |
| 5. #17987322 | C3 | semidirect |
| 6. #17987319 | C3 | semidirect |
| 7. #17987316 | C3 | semidirect |
| 8. #17987314 | C3 | semidirect |
| 9. #17987311 | C3 | semidirect |
| 10. #17987311 | C3 | semidirect |
| 11. #17987311 | C3 | semidirect |
| 13. C19×#6860 | C3 | semidirect |
| 64. #6860 | C19⋊C3 | semidirect |
| 148. C19 | #10624677 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987441 | 3 |
| #17987435 | 3 |
| #17987432 | 3 |
| #17987427 | 3 |
| #17987322 | 3 |
| #17987319 | 3 |
| #17987316 | 3 |
| #17987314 | 3 |
| #17987311 | 3 |
| #17987310 | 3 |
| C19×#6860 | 3 |
| #10624677 | 19 |