Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
584 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 137 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×#13133245 | C2 | semidirect |
| 2. C2×#13133243 | C2 | semidirect |
| 3. C2×#13133213 | C2 | semidirect |
| 4. #16811091 | C2 | semidirect |
| 5. #16810822 | C2 | semidirect |
| 6. #16810817 | C2 | semidirect |
| 7. #16810646 | C2 | semidirect |
| 8. #16810627 | C2 | semidirect |
| 9. C53×#418 | C2 | semidirect |
| 15. C2×#11719913 | C22 | semidirect |
| 16. C2×#11719923 | C22 | semidirect |
| 17. C2×D424 | C22 | semidirect |
| 18. C2×#11719922 | C22 | semidirect |
| 23. #13133182 | C22 | semidirect |
| 24. #13133179 | C22 | semidirect |
| 29. #13133146 | C22 | semidirect |
| 30. #13133137 | C22 | semidirect |
| 34. #102×C53 | C22 | semidirect |
| 48. #11719945 | D4 | semidirect |
| 101. D212 | C2×D4 | semidirect |
| 105. Dic106 | C2×D4 | semidirect |
| 125. Dic53 | AGL(1,ℤ/8) | semidirect |
| 141. #418 | D53 | semidirect |
| 142. C53 | #3038 | semidirect |
| 167. #102 | C2×D53 | semidirect |