Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#13133223 | C2 | semidirect |
| 2. #16811197 | C2 | semidirect |
| 4. #16810866 | C2 | semidirect |
| 5. #16810849 | C2 | semidirect |
| 6. #16810661 | C2 | semidirect |
| 7. #16810632 | C2 | semidirect |
| 8. #16810628 | C2 | semidirect |
| 9. C22×SD16×C53 | C2 | semidirect |
| 13. C2×#11719912 | C22 | semidirect |
| 14. C2×C8×D53 | C22 | semidirect |
| 20. #13133193 | C22 | semidirect |
| 25. #13133151 | C22 | semidirect |
| 26. #13133149 | C22 | semidirect |
| 27. #13133141 | C22 | semidirect |
| 55. C2×C8×C53 | D4 | semidirect |
| 121. C22×SD16 | D53 | semidirect |
| 130. C53 | #3057 | semidirect |
| 180. C2×C8 | C22⋊D53 | semidirect |