Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
198 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 46 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. C19⋊C3×#733 | C3 | semidirect |
| 2. C19⋊C3×#733 | C3 | semidirect |
| 4. #17987404 | C3 | semidirect |
| 5. #17987392 | C3 | semidirect |
| 6. #17987391 | C3 | semidirect |
| 7. #17987390 | C3 | semidirect |
| 8. #17987390 | C3 | semidirect |
| 9. #17987389 | C3 | semidirect |
| 10. #17987389 | C3 | semidirect |
| 11. #17987388 | C3 | semidirect |
| 12. #17987388 | C3 | semidirect |
| 13. C19×#6883 | C3 | semidirect |
| 18. #13095322 | C32 | semidirect |
| 19. #13095322 | C32 | semidirect |
| 20. #13095322 | C32 | semidirect |
| 21. #13095322 | C32 | semidirect |
| 30. #13095307 | C32 | semidirect |
| 31. #13095306 | C32 | semidirect |
| 35. C19×#733 | C32 | semidirect |
| 36. C19×#733 | C32 | semidirect |
| 38. C19×C9⋊C9 | C32 | semidirect |
| 80. #6883 | C19⋊C3 | semidirect |
| 114. #733 | C3×C19⋊C3 | semidirect |
| 115. #733 | C3×C19⋊C3 | semidirect |
| 124. C9⋊C9 | C3×C19⋊C3 | semidirect |
| 163. C19 | #10624848 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C19⋊C3×#733 | 3 |
| C19⋊C3×#732 | 3 |
| #17987404 | 3 |
| #17987392 | 3 |
| #17987391 | 3 |
| #17987390 | 3 |
| #17987389 | 3 |
| #17987388 | 3 |
| C19×#6883 | 3 |
| #10624848 | 19 |