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×#13095333 | C3 | semidirect |
| 4. #17987511 | C3 | semidirect |
| 5. #17987510 | C3 | semidirect |
| 6. #17987509 | C3 | semidirect |
| 7. #17987508 | C3 | semidirect |
| 8. #17987507 | C3 | semidirect |
| 9. C3×#13095318 | C3 | semidirect |
| 10. C3×#13095316 | C3 | semidirect |
| 11. C19⋊C3×#731 | C3 | semidirect |
| 12. C19×#6910 | C3 | semidirect |
| 18. C3×#10587025 | C32 | semidirect |
| 19. C3×#10587025 | C32 | semidirect |
| 20. C3×#10587025 | C32 | semidirect |
| 21. C3×#10587022 | C32 | semidirect |
| 22. C3×#10587023 | C32 | semidirect |
| 23. 3−1+2×C19⋊C3 | C32 | semidirect |
| 29. C32×#4294 | C32 | semidirect |
| 30. C3×C9×C19⋊C3 | C32 | semidirect |
| 31. #13095318 | C32 | semidirect |
| 32. #13095318 | C32 | semidirect |
| 33. #13095318 | C32 | semidirect |
| 34. #13095318 | C32 | semidirect |
| 35. #13095317 | C32 | semidirect |
| 36. #13095316 | C32 | semidirect |
| 37. #13095316 | C32 | semidirect |
| 38. #13095316 | C32 | semidirect |
| 39. #13095316 | C32 | semidirect |
| 40. C3×C19×3−1+2 | C32 | semidirect |
| 41. C3×C19×3−1+2 | C32 | semidirect |
| 43. C19×#731 | C32 | semidirect |
| 95. #6910 | C19⋊C3 | semidirect |
| 129. C3×3−1+2 | C3×C19⋊C3 | semidirect |
| 130. C3×3−1+2 | C3×C19⋊C3 | semidirect |
| 148. #731 | C3×C19⋊C3 | semidirect |
| 198. 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×#13095333 | 3 |
| #17987511 | 3 |
| #17987510 | 3 |
| #17987509 | 3 |
| #17987508 | 3 |
| #17987507 | 3 |
| C3×#13095318 | 3 |
| C3×#13095316 | 3 |
| C19⋊C3×#731 | 3 |
| C19×#6910 | 3 |
| #10624931 | 19 |