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×#13133264 | C2 | semidirect |
| 2. C2×#13133242 | C2 | semidirect |
| 3. C22×#11719913 | C2 | semidirect |
| 4. #16811192 | C2 | semidirect |
| 5. #16810769 | C2 | semidirect |
| 6. #16810763 | C2 | semidirect |
| 7. #16810631 | C2 | semidirect |
| 8. #16810589 | C2 | semidirect |
| 9. C53×#416 | C2 | semidirect |
| 15. C2×#11719947 | C22 | semidirect |
| 18. C2×Q8×D53 | C22 | semidirect |
| 30. #13133140 | C22 | semidirect |
| 31. #13133129 | C22 | semidirect |
| 35. #103×C53 | C22 | semidirect |
| 36. #102×C53 | C22 | semidirect |
| 39. #41×C53 | D4 | semidirect |
| 70. C2×Dic106 | D4 | semidirect |
| 153. #416 | D53 | semidirect |
| 155. C53 | #3010 | semidirect |
| 180. #103 | C2×D53 | semidirect |
| 181. #102 | C2×D53 | semidirect |
| 191. #41 | D212 | semidirect |