Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
548 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 143 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×M16×D53 | C2 | semidirect |
| 3. #16811135 | C2 | semidirect |
| 4. C2×#13133192 | C2 | semidirect |
| 5. #16810877 | C2 | semidirect |
| 6. #16810870 | C2 | semidirect |
| 7. #16810860 | C2 | semidirect |
| 8. #16810853 | C2 | semidirect |
| 9. #16810627 | C2 | semidirect |
| 10. #16810622 | C2 | semidirect |
| 11. C53×#428 | C2 | semidirect |
| 17. C2×#11719913 | C22 | semidirect |
| 18. C2×D424 | C22 | semidirect |
| 20. C2×#11719912 | C22 | semidirect |
| 22. C2×C8×D53 | C22 | semidirect |
| 24. #13133197 | C22 | semidirect |
| 25. #13133197 | C22 | semidirect |
| 30. #13133192 | C22 | semidirect |
| 31. #13133192 | C22 | semidirect |
| 36. #13133140 | C22 | semidirect |
| 37. #13133137 | C22 | semidirect |
| 38. #13133137 | C22 | semidirect |
| 39. #13133137 | C22 | semidirect |
| 43. #107×C53 | C22 | semidirect |
| 44. #106×C53 | C22 | semidirect |
| 71. M16×C53 | D4 | semidirect |
| 135. C8×C53 | C2×D4 | semidirect |
| 154. C2×D53 | AGL(1,ℤ/8) | semidirect |
| 181. #428 | D53 | semidirect |
| 184. C53 | #3055 | semidirect |
| 212. #107 | C2×D53 | semidirect |
| 213. #106 | C2×D53 | semidirect |
| 248. M16 | D212 | semidirect |
| 309. C8 | C2×D212 | semidirect |