Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
1148 conjugacy classes of subgroups; only the 468 normal subgroups are shown.
This group has 1148 conjugacy classes of subgroups — too many to draw. Only its 468 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. 3−1+2×#4296 | C3 | direct (N × H) |
| 3. C3×#13095339 | C3 | semidirect |
| 4. C3×#13095338 | C3 | semidirect |
| 6. C3×C9×#4296 | C3 | semidirect |
| 14. #13095339 | C32 | semidirect |
| 15. #13095338 | C32 | semidirect |
| 17. C9×#4296 | C32 | semidirect |
| 19. C3×#10587025 | C9 | semidirect |
| 20. C3×#10587022 | C9 | semidirect |
| 21. C3×#10587023 | C9 | semidirect |
| 22. 3−1+2×C19⋊C3 | C9 | semidirect |
| 25. C3×C19×3−1+2 | C9 | semidirect |
| 39. C3×#4296 | 3−1+2 | direct (N × H) |
| 44. C19×3−1+2 | C3×C9 | semidirect |
| 45. C3×C9×C19 | C3×C9 | semidirect |
| 46. #10587025 | C3×C9 | semidirect |
| 47. C3×#4294 | C3×C9 | semidirect |
| 48. #10587023 | C3×C9 | semidirect |
| 49. #10587022 | C3×C9 | semidirect |
| 50. C9×C19⋊C3 | C3×C9 | semidirect |
| 76. #4296 | C3×3−1+2 | direct (N × H) |
| 77. C9×C19 | C32×C9 | semidirect |
| 78. #4294 | C32×C9 | semidirect |
| 85. C3×3−1+2 | #4296 | direct (N × H) |
| 98. C3×C19 | C9×3−1+2 | semidirect |
| 102. C19⋊C3 | C9×3−1+2 | semidirect |
| 116. 3−1+2 | C3×#4296 | direct (N × H) |
| 129. C3×C9 | C3×#4296 | semidirect |
| 130. C19 | C3×C9×3−1+2 | semidirect |
| 150. C9 | C32×#4296 | semidirect |
| 157. C3 | 3−1+2×#4296 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#4296 | 3 |
| 3−1+2×#4296 | 3 |
| C3×#13095339 | 3 |
| C3×#13095338 | 3 |
| C3×C32⋊#4296 | 3 |
| C3×C9×#4296 | 3 |
| C3×3−1+2×C19⋊C3 | 3 |
| C3×C9×3−1+2 | 19 |