Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
716 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 716 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 |
|---|---|---|
| 2. #17987468 | C3 | semidirect |
| 3. #17987468 | C3 | semidirect |
| 4. #17987467 | C3 | semidirect |
| 5. #17987466 | C3 | semidirect |
| 6. #17987465 | C3 | semidirect |
| 7. #17987464 | C3 | semidirect |
| 8. #17987463 | C3 | semidirect |
| 9. #17987462 | C3 | semidirect |
| 10. #17987444 | C3 | semidirect |
| 12. #17987404 | C3 | semidirect |
| 13. #17987403 | C3 | semidirect |
| 14. C19×#6900 | C3 | semidirect |
| 25. #13095307 | C32 | semidirect |
| 26. #13095307 | C32 | semidirect |
| 27. #13095306 | C32 | semidirect |
| 28. #13095306 | C32 | semidirect |
| 29. #13095305 | C32 | semidirect |
| 30. #13095305 | C32 | semidirect |
| 31. #13095305 | C32 | semidirect |
| 32. #13095305 | C32 | semidirect |
| 33. #13095305 | C32 | semidirect |
| 34. #13095305 | C32 | semidirect |
| 35. #13095305 | C32 | semidirect |
| 42. C9×#4294 | C32 | semidirect |
| 43. C9×#4294 | C32 | semidirect |
| 46. C19×C9⋊C9 | C32 | semidirect |
| 47. C19×C9⋊C9 | C32 | semidirect |
| 48. C92×C19 | C32 | semidirect |
| 75. C9×C19⋊C3 | 3−1+2 | semidirect |
| 79. #6900 | C19⋊C3 | semidirect |
| 133. C9⋊C9 | C3×C19⋊C3 | semidirect |
| 134. C9⋊C9 | C3×C19⋊C3 | semidirect |
| 143. C92 | C3×C19⋊C3 | semidirect |
| 176. C19 | #10624884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×3−1+2×C19⋊C3 | 3 |
| #17987468 | 3 |
| #17987467 | 3 |
| #17987466 | 3 |
| #17987465 | 3 |
| #17987464 | 3 |
| #17987463 | 3 |
| #17987462 | 3 |
| #17987444 | 3 |
| #17987418 | 3 |
| #17987404 | 3 |
| #17987403 | 3 |
| C19×#6900 | 3 |
| #10624884 | 19 |