Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
980 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 980 conjugacy classes of subgroups — too many to draw. Only its 286 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. #17987546 | C3 | semidirect |
| 2. #17987528 | C3 | semidirect |
| 3. #17987519 | C3 | semidirect |
| 4. #17987515 | C3 | semidirect |
| 5. #17987510 | C3 | semidirect |
| 6. #17987500 | C3 | semidirect |
| 7. C3×#13095314 | C3 | semidirect |
| 8. C32×C19×3−1+2 | C3 | semidirect |
| 10. #13095332 | C32 | semidirect |
| 14. #13095322 | C32 | semidirect |
| 15. #13095320 | C32 | semidirect |
| 16. #13095317 | C32 | semidirect |
| 17. #13095314 | C32 | semidirect |
| 18. #13095314 | C32 | semidirect |
| 24. C3×C19×3−1+2 | C32 | semidirect |
| 25. C32×C9×C19 | C32 | semidirect |
| 51. C32×3−1+2 | C19⋊C3 | semidirect |
| 81. C3×3−1+2 | C3×C19⋊C3 | semidirect |
| 83. C32×C9 | C3×C19⋊C3 | semidirect |
| 118. C19 | #10624934 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987546 | 3 |
| #17987528 | 3 |
| #17987519 | 3 |
| #17987515 | 3 |
| #17987510 | 3 |
| #17987500 | 3 |
| C3×#13095314 | 3 |
| C32×C19×3−1+2 | 3 |
| #10624934 | 19 |