Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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. #16811176 | C2 | semidirect |
| 3. #16810984 | C2 | semidirect |
| 4. #16810979 | C2 | semidirect |
| 5. #16810632 | C2 | semidirect |
| 8. M16×Dic53 | C2 | semidirect |
| 9. C53×#419 | C2 | semidirect |
| 12. #13133216 | C22 | semidirect |
| 13. #13133208 | C22 | semidirect |
| 22. #13133141 | C22 | semidirect |
| 25. #13133127 | C22 | semidirect |
| 26. C8×Dic53 | C22 | semidirect |
| 30. #103×C53 | C22 | semidirect |
| 110. #419 | D53 | semidirect |
| 114. C53 | #3140 | semidirect |
| 131. #103 | C2×D53 | semidirect |