Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
978 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 978 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 |
| 3. C3×#13095332 | C3 | semidirect |
| 4. #17987511 | C3 | semidirect |
| 5. #17987509 | C3 | semidirect |
| 6. #17987508 | C3 | semidirect |
| 7. #17987507 | C3 | semidirect |
| 8. C3×#13095317 | C3 | semidirect |
| 9. C19⋊C3×#731 | C3 | semidirect |
| 10. C3×C19×#731 | C3 | semidirect |
| 15. C3×#10587025 | C32 | semidirect |
| 16. C3×#10587025 | C32 | semidirect |
| 17. C3×#10587022 | C32 | semidirect |
| 18. C3×#10587023 | C32 | semidirect |
| 19. 3−1+2×C19⋊C3 | C32 | semidirect |
| 25. C3×C9×C19⋊C3 | C32 | semidirect |
| 26. #13095318 | C32 | semidirect |
| 27. #13095317 | C32 | semidirect |
| 28. #13095317 | C32 | semidirect |
| 29. #13095317 | C32 | semidirect |
| 30. #13095316 | C32 | semidirect |
| 31. C3×C19×3−1+2 | C32 | semidirect |
| 33. C32×C9×C19 | C32 | semidirect |
| 34. C19×#731 | C32 | semidirect |
| 35. C19×#731 | C32 | semidirect |
| 36. C19×#731 | C32 | semidirect |
| 81. C3×#731 | C19⋊C3 | semidirect |
| 108. C3×3−1+2 | C3×C19⋊C3 | semidirect |
| 116. C32×C9 | C3×C19⋊C3 | semidirect |
| 122. #731 | C3×C19⋊C3 | semidirect |
| 123. #731 | C3×C19⋊C3 | semidirect |
| 124. #731 | C3×C19⋊C3 | semidirect |
| 166. C19 | #10624931 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987546 | 3 |
| C19⋊H(5,𝔽3) | 3 |
| C3×#13095332 | 3 |
| #17987511 | 3 |
| #17987509 | 3 |
| #17987508 | 3 |
| #17987507 | 3 |
| C3×#13095317 | 3 |
| C19⋊C3×#731 | 3 |
| C3×C19×#731 | 3 |
| #10624931 | 19 |