Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13133265 | C2 | semidirect |
| 2. C2×#13133245 | C2 | semidirect |
| 3. C22×#11719924 | C2 | semidirect |
| 4. #16811192 | C2 | semidirect |
| 5. #16810771 | C2 | semidirect |
| 6. #16810763 | C2 | semidirect |
| 7. #16810617 | C2 | semidirect |
| 8. #16810591 | C2 | semidirect |
| 9. C53×#419 | C2 | semidirect |
| 13. C2×#11719949 | C22 | semidirect |
| 18. C2×Q8×D53 | C22 | semidirect |
| 30. #13133140 | C22 | semidirect |
| 31. #13133137 | C22 | semidirect |
| 32. #13133129 | C22 | semidirect |
| 36. #103×C53 | C22 | semidirect |
| 40. C2×Q8×C53 | D4 | semidirect |
| 56. #11719945 | D4 | semidirect |
| 152. #419 | D53 | semidirect |
| 155. C53 | #3010 | semidirect |
| 180. #103 | C2×D53 | semidirect |
| 200. C2×Q8 | D212 | semidirect |