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×M16×D53 | C2 | semidirect |
| 2. #16811130 | C2 | semidirect |
| 3. C2×#13133188 | C2 | semidirect |
| 4. #16810873 | C2 | semidirect |
| 5. #16810866 | C2 | semidirect |
| 6. #16810856 | C2 | semidirect |
| 7. #16810849 | C2 | semidirect |
| 8. #16810665 | C2 | semidirect |
| 9. #16810628 | C2 | semidirect |
| 10. #16810624 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C53 | C2 | semidirect |
| 15. C2×#11719912 | C22 | semidirect |
| 17. C2×C8×D53 | C22 | semidirect |
| 19. #13133193 | C22 | semidirect |
| 20. #13133193 | C22 | semidirect |
| 25. #13133188 | C22 | semidirect |
| 26. #13133188 | C22 | semidirect |
| 33. #13133151 | C22 | semidirect |
| 34. #13133149 | C22 | semidirect |
| 35. #13133141 | C22 | semidirect |
| 36. #13133138 | C22 | semidirect |
| 37. #13133138 | C22 | semidirect |
| 38. #13133138 | C22 | semidirect |
| 42. C2×SD16×C53 | C22 | semidirect |
| 43. C2×D8×C53 | C22 | semidirect |
| 73. M16×C53 | D4 | semidirect |
| 135. C8×C53 | C2×D4 | semidirect |
| 154. C2×D53 | AGL(1,ℤ/8) | semidirect |
| 173. C2×AGL(1,ℤ/8) | D53 | semidirect |
| 184. C53 | #3055 | semidirect |
| 190. C2×SD16 | C2×D53 | semidirect |
| 191. C2×D8 | C2×D53 | semidirect |
| 248. M16 | C22⋊D53 | semidirect |
| 309. C8 | C2×C22⋊D53 | semidirect |