Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #16811251 | C2 | semidirect |
| 2. #16810987 | C2 | semidirect |
| 3. #16810982 | C2 | semidirect |
| 4. #16810977 | C2 | semidirect |
| 5. #16810969 | C2 | semidirect |
| 6. #16810628 | C2 | semidirect |
| 7. #16810624 | C2 | semidirect |
| 8. #16810619 | C2 | semidirect |
| 9. C2×#13133138 | C2 | semidirect |
| 10. #16810579 | C2 | semidirect |
| 14. #13133217 | C22 | semidirect |
| 16. #13133209 | C22 | semidirect |
| 21. #13133141 | C22 | semidirect |
| 22. #13133141 | C22 | semidirect |
| 23. #13133141 | C22 | semidirect |
| 28. #13133138 | C22 | semidirect |
| 29. #13133138 | C22 | semidirect |
| 30. #13133138 | C22 | semidirect |
| 31. #13133128 | C22 | semidirect |
| 32. C4×#88322 | C22 | semidirect |
| 147. C53 | #3136 | semidirect |