Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
584 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 145 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×#13133242 | C2 | semidirect |
| 2. C2×#13133213 | C2 | semidirect |
| 3. #41×Dic53 | C2 | semidirect |
| 4. #16810821 | C2 | semidirect |
| 5. #16810816 | C2 | semidirect |
| 6. #16810646 | C2 | semidirect |
| 7. #16810629 | C2 | semidirect |
| 8. #16810628 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C53 | C2 | semidirect |
| 13. C2×#11719924 | C22 | semidirect |
| 14. C2×#11719922 | C22 | semidirect |
| 19. Q8×Dic53 | C22 | semidirect |
| 21. D4×Dic53 | C22 | semidirect |
| 26. #13133146 | C22 | semidirect |
| 27. #13133139 | C22 | semidirect |
| 28. #13133138 | C22 | semidirect |
| 32. C2×SD16×C53 | C22 | semidirect |
| 33. C2×D8×C53 | C22 | semidirect |
| 38. #41×C53 | D4 | semidirect |
| 83. Q8×C53 | C2×D4 | semidirect |
| 89. D4×C53 | C2×D4 | semidirect |
| 125. Dic53 | AGL(1,ℤ/8) | semidirect |
| 134. C2×AGL(1,ℤ/8) | D53 | semidirect |
| 142. C53 | #3038 | semidirect |
| 150. C2×SD16 | C2×D53 | semidirect |
| 152. C2×D8 | C2×D53 | semidirect |
| 171. #41 | C22⋊D53 | semidirect |
| 216. Q8 | C2×C22⋊D53 | semidirect |
| 227. D4 | C2×C22⋊D53 | semidirect |