Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
944 conjugacy classes of subgroups; only the 454 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 454 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. C9×#10587022 | C3 | semidirect |
| 3. #17987410 | C3 | semidirect |
| 4. #17987405 | C3 | semidirect |
| 5. #17987402 | C3 | semidirect |
| 7. C19×#6887 | C3 | semidirect |
| 9. C3×#10587022 | C9 | semidirect |
| 14. #13095307 | C32 | semidirect |
| 15. #13095306 | C32 | semidirect |
| 16. #13095305 | C32 | semidirect |
| 19. C9×#4294 | C32 | semidirect |
| 20. C9×#4294 | C32 | semidirect |
| 22. C19×C9⋊C9 | C32 | semidirect |
| 24. C92×C19 | C32 | semidirect |
| 30. C3×C9×C19 | C3×C9 | semidirect |
| 34. C3×#4294 | C3×C9 | semidirect |
| 37. #10587022 | C3×C9 | semidirect |
| 38. #10587022 | C3×C9 | semidirect |
| 45. #6887 | C19⋊C3 | semidirect |
| 69. C9⋊C9 | C3×C19⋊C3 | semidirect |
| 75. C92 | C3×C19⋊C3 | semidirect |
| 90. C3×C9 | C9×C19⋊C3 | semidirect |
| 94. C19 | #10624863 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#10587022 | 3 |
| C9×#10587022 | 3 |
| #17987410 | 3 |
| #17987405 | 3 |
| #17987402 | 3 |
| C19⋊C3×C32⋊C9 | 3 |
| C19×#6887 | 3 |
| #10624863 | 19 |