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×#13095332 | C3 | semidirect |
| 3. #17987530 | C3 | semidirect |
| 4. #17987529 | C3 | semidirect |
| 5. #17987511 | C3 | semidirect |
| 6. #17987506 | C3 | semidirect |
| 7. #17987501 | C3 | semidirect |
| 8. C3×#13095322 | C3 | semidirect |
| 9. C3×#13095320 | C3 | semidirect |
| 10. C3×C19×#733 | C3 | semidirect |
| 12. #13095333 | C32 | semidirect |
| 20. C3×#10587022 | C32 | semidirect |
| 21. C3×#10587023 | C32 | semidirect |
| 25. C3×C9×C19⋊C3 | C32 | semidirect |
| 26. #13095322 | C32 | semidirect |
| 27. #13095322 | C32 | semidirect |
| 28. #13095322 | C32 | semidirect |
| 32. #13095318 | C32 | semidirect |
| 33. #13095315 | C32 | semidirect |
| 36. C19×#733 | C32 | semidirect |
| 37. C19×#733 | C32 | semidirect |
| 38. C19×#733 | C32 | semidirect |
| 85. C3×#733 | C19⋊C3 | semidirect |
| 123. #733 | C3×C19⋊C3 | semidirect |
| 124. #733 | C3×C19⋊C3 | semidirect |
| 125. #733 | C3×C19⋊C3 | semidirect |
| 175. C19 | #10624936 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987546 | 3 |
| C3×#13095332 | 3 |
| #17987530 | 3 |
| #17987529 | 3 |
| #17987511 | 3 |
| #17987506 | 3 |
| #17987501 | 3 |
| C3×#13095322 | 3 |
| C3×#13095320 | 3 |
| C3×C19×#733 | 3 |
| #10624936 | 19 |