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×#13133243 | C2 | semidirect |
| 2. #16811169 | C2 | semidirect |
| 3. C2×D4×Dic53 | C2 | semidirect |
| 4. #16810840 | C2 | semidirect |
| 5. #16810836 | C2 | semidirect |
| 6. #16810826 | C2 | semidirect |
| 7. #16810816 | C2 | semidirect |
| 8. #16810646 | C2 | semidirect |
| 9. #16810625 | C2 | semidirect |
| 10. #16810624 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C53 | C2 | semidirect |
| 18. #13133215 | C22 | semidirect |
| 19. #13133213 | C22 | semidirect |
| 20. #13133206 | C22 | semidirect |
| 21. #13133204 | C22 | semidirect |
| 33. #13133146 | C22 | semidirect |
| 34. #13133146 | C22 | semidirect |
| 35. #13133142 | C22 | semidirect |
| 36. #13133141 | C22 | semidirect |
| 37. #13133139 | C22 | semidirect |
| 38. #13133138 | C22 | semidirect |
| 52. C2×D4×C53 | D4 | semidirect |
| 158. Dic53 | AGL(1,ℤ/8) | semidirect |
| 168. C2×AGL(1,ℤ/8) | D53 | semidirect |
| 178. C53 | #3036 | semidirect |
| 226. C2×D4 | C22⋊D53 | semidirect |