Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
692 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 271 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. #17987456 | C3 | semidirect |
| 2. #17987455 | C3 | semidirect |
| 3. #17987454 | C3 | semidirect |
| 4. #17987453 | C3 | semidirect |
| 5. #17987452 | C3 | semidirect |
| 6. C19⋊C3×C9⋊C9 | C3 | semidirect |
| 8. C92×C19⋊C3 | C3 | semidirect |
| 9. C19×#6897 | C3 | semidirect |
| 13. #13095307 | C32 | semidirect |
| 14. #13095306 | C32 | semidirect |
| 15. #13095305 | C32 | semidirect |
| 16. #13095305 | C32 | semidirect |
| 17. #13095305 | C32 | semidirect |
| 23. C9×#4294 | C32 | semidirect |
| 24. C19×C9⋊C9 | C32 | semidirect |
| 26. C92×C19 | C32 | semidirect |
| 45. #6897 | C19⋊C3 | direct (N × H) |
| 68. C9⋊C9 | C3×C19⋊C3 | semidirect |
| 76. C92 | C3×C19⋊C3 | semidirect |
| 81. C19⋊C3 | #6897 | direct (N × H) |
| 94. C19 | C3×#6897 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987456 | 3 |
| #17987455 | 3 |
| #17987454 | 3 |
| #17987453 | 3 |
| #17987452 | 3 |
| C19⋊C3×C9⋊C9 | 3 |
| C19⋊C3×C32⋊C9 | 3 |
| C92×C19⋊C3 | 3 |
| C19×#6897 | 3 |
| C3×#6897 | 19 |