Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
836 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 836 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 |
|---|---|---|
| 2. #17987445 | C3 | semidirect |
| 3. #17987444 | C3 | semidirect |
| 4. #17987443 | C3 | semidirect |
| 5. #17987442 | C3 | semidirect |
| 6. C19⋊C3×C9⋊C9 | C3 | semidirect |
| 8. C19×#6895 | C3 | semidirect |
| 16. #13095307 | C32 | semidirect |
| 17. #13095306 | C32 | semidirect |
| 18. #13095305 | C32 | semidirect |
| 19. #13095305 | C32 | semidirect |
| 20. #13095305 | C32 | semidirect |
| 24. C19×C9⋊C9 | C32 | semidirect |
| 48. #6895 | C19⋊C3 | direct (N × H) |
| 77. C9⋊C9 | C3×C19⋊C3 | semidirect |
| 85. C19⋊C3 | #6895 | direct (N × H) |
| 102. C19 | C3×#6895 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C9×C19⋊C3 | 3 |
| #17987445 | 3 |
| #17987444 | 3 |
| #17987443 | 3 |
| #17987442 | 3 |
| C19⋊C3×C9⋊C9 | 3 |
| C19⋊C3×C32⋊C9 | 3 |
| C19×#6895 | 3 |
| C3×#6895 | 19 |