Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
692 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 292 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. #17987452 | C3 | direct (N × H) |
| 2. C3×#13095307 | C3 | semidirect |
| 3. C3×#13095306 | C3 | semidirect |
| 4. C3×#13095305 | C3 | semidirect |
| 5. C3×#13095305 | C3 | semidirect |
| 6. C3×#13095305 | C3 | semidirect |
| 7. C3×#13095305 | C3 | semidirect |
| 8. C3×#13095305 | C3 | semidirect |
| 9. C3×#13095305 | C3 | semidirect |
| 13. C3×C9×#4294 | C3 | semidirect |
| 24. #13095307 | C32 | semidirect |
| 25. #13095306 | C32 | semidirect |
| 26. #13095305 | C32 | semidirect |
| 27. #13095305 | C32 | semidirect |
| 28. #13095305 | C32 | semidirect |
| 29. #13095305 | C32 | semidirect |
| 30. #13095305 | C32 | semidirect |
| 31. #13095305 | C32 | semidirect |
| 35. C9×#4294 | C32 | semidirect |
| 135. C3×C19 | #6897 | semidirect |
| 170. C19 | C3×#6897 | semidirect |
| 194. C3 | #17987452 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987452 | 3 |
| C3×#13095307 | 3 |
| C3×#13095306 | 3 |
| C3×#13095305 | 3 |
| C3×C32⋊#4294 | 3 |
| C3×C9×#4294 | 3 |
| C3×C19×C32⋊C9 | 3 |
| C3×#6897 | 19 |