Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
320 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 150 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 |
|---|---|---|
| 3. #17987554 | C3 | semidirect |
| 4. #17987553 | C3 | semidirect |
| 5. C27×#4296 | C3 | semidirect |
| 8. #13095344 | C9 | semidirect |
| 9. #13095343 | C9 | semidirect |
| 10. #13095342 | C9 | semidirect |
| 17. #13095312 | C9 | semidirect |
| 18. #13095311 | C9 | semidirect |
| 19. #13095310 | C9 | semidirect |
| 21. C19×C27⋊C3 | C9 | semidirect |
| 36. #10587020 | C3×C9 | semidirect |
| 37. C19×C27 | C3×C9 | semidirect |
| 38. #10587018 | C3×C9 | semidirect |
| 52. #4296 | C27⋊C3 | direct (N × H) |
| 66. C27⋊C3 | #4296 | direct (N × H) |
| 93. C27 | C3×#4296 | semidirect |
| 94. C19 | C9×C27⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| (C19⋊C3)⋊(C27⋊C3) | 3 |
| C3×C9×#4296 | 3 |
| #17987554 | 3 |
| #17987553 | 3 |
| C27×#4296 | 3 |
| C19⋊C3×C27⋊C3 | 3 |
| C9×C27⋊C3 | 19 |