Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
1064 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 1064 conjugacy classes of subgroups — too many to draw. Only its 274 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. C3×#13095333 | C3 | semidirect |
| 2. C3×#13095331 | C3 | semidirect |
| 3. C32×C9×C19⋊C3 | C3 | semidirect |
| 4. #17987499 | C3 | direct (N × H) |
| 5. C3×#13095321 | C3 | semidirect |
| 6. C3×#13095319 | C3 | semidirect |
| 7. C3×#13095317 | C3 | semidirect |
| 8. C3×#13095315 | C3 | semidirect |
| 9. C3×#13095313 | C3 | semidirect |
| 10. C3×C19×#731 | C3 | semidirect |
| 13. #13095333 | C32 | semidirect |
| 15. #13095331 | C32 | semidirect |
| 29. C3×C9×C19⋊C3 | C32 | semidirect |
| 30. #13095321 | C32 | semidirect |
| 31. #13095319 | C32 | semidirect |
| 32. #13095317 | C32 | semidirect |
| 33. #13095315 | C32 | semidirect |
| 34. #13095313 | C32 | semidirect |
| 38. C19×#731 | C32 | semidirect |
| 84. C3×#731 | C19⋊C3 | semidirect |
| 131. #731 | C3×C19⋊C3 | semidirect |
| 137. C3×C19 | #6908 | semidirect |
| 178. C19 | C3×#6908 | semidirect |
| 203. C3 | #17987499 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#13095333 | 3 |
| C3×#13095331 | 3 |
| C32×C9×C19⋊C3 | 3 |
| #17987499 | 3 |
| C3×#13095321 | 3 |
| C3×#13095319 | 3 |
| C3×#13095317 | 3 |
| C3×#13095315 | 3 |
| C3×#13095313 | 3 |
| C3×C19×#731 | 3 |
| C3×#6908 | 19 |