Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
986 conjugacy classes of subgroups; only the 438 normal subgroups are shown.
This group has 986 conjugacy classes of subgroups — too many to draw. Only its 438 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. 3−1+2×#4296 | C3 | semidirect |
| 3. #17987589 | C3 | semidirect |
| 4. C3×C9×#4296 | C3 | semidirect |
| 13. #13095333 | C9 | semidirect |
| 14. #13095332 | C9 | semidirect |
| 15. #13095331 | C9 | semidirect |
| 19. C19×#737 | C9 | semidirect |
| 25. C19×3−1+2 | C3×C9 | semidirect |
| 27. C3×C9×C19 | C3×C9 | semidirect |
| 29. #10587025 | C3×C9 | semidirect |
| 30. C3×#4294 | C3×C9 | semidirect |
| 31. #10587023 | C3×C9 | semidirect |
| 32. #10587022 | C3×C9 | semidirect |
| 33. C9×C19⋊C3 | C3×C9 | semidirect |
| 34. C9×C19⋊C3 | C3×C9 | semidirect |
| 47. #4296 | #737 | direct (N × H) |
| 55. #737 | #4296 | direct (N × H) |
| 74. 3−1+2 | C3×#4296 | semidirect |
| 85. C3×C9 | C3×#4296 | semidirect |
| 86. C19 | C9×#737 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| 3−1+2×#4296 | 3 |
| H(3,𝔽3)×#4296 | 3 |
| #17987589 | 3 |
| C3×C9×#4296 | 3 |
| C19⋊C3×#737 | 3 |
| C9×#737 | 19 |