Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 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 |
| 3. #16810926 | C2 | semidirect |
| 4. #16810922 | C2 | semidirect |
| 5. #16810912 | C2 | semidirect |
| 6. #16810902 | C2 | semidirect |
| 7. #16810666 | C2 | semidirect |
| 8. #16810649 | C2 | semidirect |
| 11. C53×#427 | C2 | semidirect |
| 15. #13133216 | C22 | semidirect |
| 17. #13133208 | C22 | semidirect |
| 26. #13133150 | C22 | semidirect |
| 27. #13133148 | C22 | semidirect |
| 28. #13133146 | C22 | semidirect |
| 29. #13133146 | C22 | semidirect |
| 37. #107×C53 | C22 | semidirect |
| 38. #107×C53 | C22 | semidirect |
| 39. #106×C53 | C22 | semidirect |
| 40. #106×C53 | C22 | semidirect |
| 46. C2×D212 | Q8 | semidirect |
| 132. #427 | D53 | semidirect |
| 136. C53 | #3081 | semidirect |
| 155. #107 | C2×D53 | semidirect |
| 156. #107 | C2×D53 | semidirect |
| 158. #106 | C2×D53 | semidirect |
| 159. #106 | C2×D53 | semidirect |