Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
948 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 948 conjugacy classes of subgroups — too many to draw. Only its 286 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. #17987523 | C3 | semidirect |
| 4. #17987522 | C3 | semidirect |
| 5. #17987518 | C3 | semidirect |
| 6. #17987514 | C3 | semidirect |
| 7. #17987506 | C3 | semidirect |
| 8. #17987504 | C3 | semidirect |
| 9. #17987497 | C3 | semidirect |
| 10. C3×#13095318 | C3 | semidirect |
| 11. C3×#13095316 | C3 | semidirect |
| 12. C19×3−1+4 | C3 | semidirect |
| 17. #13095332 | C32 | semidirect |
| 21. C3×#10587022 | C32 | semidirect |
| 22. C3×#10587023 | C32 | semidirect |
| 27. C3×C9×C19⋊C3 | C32 | semidirect |
| 28. #13095321 | C32 | semidirect |
| 30. #13095318 | C32 | semidirect |
| 31. #13095318 | C32 | semidirect |
| 32. #13095318 | C32 | semidirect |
| 33. #13095316 | C32 | semidirect |
| 34. #13095316 | C32 | semidirect |
| 35. #13095316 | C32 | semidirect |
| 36. #13095315 | C32 | semidirect |
| 37. #13095313 | C32 | semidirect |
| 39. C19×#737 | C32 | semidirect |
| 88. 3−1+4 | C19⋊C3 | semidirect |
| 123. #737 | C3×C19⋊C3 | semidirect |
| 197. 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 |
| #17987523 | 3 |
| #17987522 | 3 |
| #17987518 | 3 |
| #17987514 | 3 |
| #17987506 | 3 |
| #17987504 | 3 |
| #17987497 | 3 |
| C3×#13095318 | 3 |
| C3×#13095316 | 3 |
| C19×3−1+4 | 3 |
| #10624935 | 19 |