Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
1232 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 1232 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. C3×3−1+2×C19⋊C3 | C3 | semidirect |
| 3. C32×C9×C19⋊C3 | C3 | semidirect |
| 4. #17987432 | C3 | semidirect |
| 5. #17987431 | C3 | semidirect |
| 6. #17987430 | C3 | semidirect |
| 7. #17987429 | C3 | semidirect |
| 8. C19⋊C3×C32⋊C9 | C3 | semidirect |
| 9. C19×#6893 | C3 | semidirect |
| 12. C3×#10587025 | C32 | semidirect |
| 13. C3×#10587022 | C32 | semidirect |
| 14. C3×#10587023 | C32 | semidirect |
| 19. C32×#4294 | C32 | semidirect |
| 23. C3×C9×C19⋊C3 | C32 | semidirect |
| 24. C32⋊#4294 | C32 | semidirect |
| 25. #13095303 | C32 | semidirect |
| 26. #13095303 | C32 | semidirect |
| 27. C3×C19×3−1+2 | C32 | semidirect |
| 29. C32×C9×C19 | C32 | semidirect |
| 30. C19×C32⋊C9 | C32 | semidirect |
| 64. #6893 | C19⋊C3 | direct (N × H) |
| 89. C3×3−1+2 | C3×C19⋊C3 | semidirect |
| 99. C32×C9 | C3×C19⋊C3 | semidirect |
| 103. C32⋊C9 | C3×C19⋊C3 | semidirect |
| 110. C19⋊C3 | #6893 | direct (N × H) |
| 136. C19 | C3×#6893 | 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 |
| C3×H(3,𝔽3)×C19⋊C3 | 3 |
| C32×C9×C19⋊C3 | 3 |
| #17987432 | 3 |
| #17987431 | 3 |
| #17987430 | 3 |
| #17987429 | 3 |
| C19⋊C3×C32⋊C9 | 3 |
| C19×#6893 | 3 |
| C3×#6893 | 19 |