Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
926 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 926 conjugacy classes of subgroups — too many to draw. Only its 274 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. #17987424 | C3 | semidirect |
| 3. #17987422 | C3 | semidirect |
| 4. #17987421 | C3 | semidirect |
| 5. #17987420 | C3 | semidirect |
| 6. #17987419 | C3 | semidirect |
| 7. C19⋊C3×C32⋊C9 | C3 | semidirect |
| 8. C19×#6891 | C3 | semidirect |
| 12. C3×#10587025 | C32 | semidirect |
| 13. C3×#10587022 | C32 | semidirect |
| 14. C3×#10587023 | C32 | semidirect |
| 18. C3×C9×C19⋊C3 | C32 | semidirect |
| 20. C32⋊#4294 | C32 | semidirect |
| 21. C32⋊#4294 | C32 | semidirect |
| 22. #13095303 | C32 | semidirect |
| 23. #13095303 | C32 | semidirect |
| 24. #13095303 | C32 | semidirect |
| 26. C3×C19×3−1+2 | C32 | semidirect |
| 28. C19×C32⋊C9 | C32 | semidirect |
| 44. C32×C19⋊C3 | 3−1+2 | semidirect |
| 63. #6891 | C19⋊C3 | semidirect |
| 97. C3×3−1+2 | C3×C19⋊C3 | semidirect |
| 109. C32⋊C9 | C3×C19⋊C3 | semidirect |
| 146. C19 | #10624883 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C32⋊(C19⋊C3) | 3 |
| #17987424 | 3 |
| #17987422 | 3 |
| #17987421 | 3 |
| #17987420 | 3 |
| #17987419 | 3 |
| C19⋊C3×C32⋊C9 | 3 |
| C19×#6891 | 3 |
| #10624883 | 19 |