Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
1232 conjugacy classes of subgroups; only the 328 normal subgroups are shown.
This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 328 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. C32×#10587025 | C3 | semidirect |
| 3. C33×#4294 | C3 | semidirect |
| 4. #17987432 | C3 | direct (N × H) |
| 5. C3×#13095303 | C3 | semidirect |
| 6. C32×C19×3−1+2 | C3 | semidirect |
| 9. C3×#10587025 | C32 | semidirect |
| 15. C32×#4294 | C32 | semidirect |
| 16. #13095303 | C32 | semidirect |
| 19. C3×C19×3−1+2 | C32 | semidirect |
| 40. C32×3−1+2 | C19⋊C3 | semidirect |
| 62. C3×3−1+2 | C3×C19⋊C3 | semidirect |
| 72. C3×C19 | #6893 | semidirect |
| 93. C19 | C3×#6893 | semidirect |
| 108. C3 | #17987432 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#10587025 | 3 |
| C32×C32⋊(C19⋊C3) | 3 |
| C33×#4294 | 3 |
| #17987432 | 3 |
| C3×#13095303 | 3 |
| C32×C19×3−1+2 | 3 |
| C3×#6893 | 19 |