Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
764 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13133262 | C2 | semidirect |
| 2. C2×#13133237 | C2 | semidirect |
| 3. #16811201 | C2 | semidirect |
| 4. #16810782 | C2 | semidirect |
| 5. #16810772 | C2 | semidirect |
| 6. #16810765 | C2 | semidirect |
| 7. #16810755 | C2 | semidirect |
| 8. #16810625 | C2 | semidirect |
| 9. C2×#13133138 | C2 | semidirect |
| 10. #16810591 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C53 | C2 | semidirect |
| 22. C2×#11719925 | C22 | semidirect |
| 23. C2×#11719923 | C22 | semidirect |
| 24. C2×#11719924 | C22 | semidirect |
| 25. C2×#11719922 | C22 | semidirect |
| 26. C22×#88322 | C22 | semidirect |
| 28. #13133193 | C22 | semidirect |
| 31. #13133188 | C22 | semidirect |
| 32. C2×C4⋊Dic53 | C22 | semidirect |
| 33. #13133142 | C22 | semidirect |
| 34. #13133139 | C22 | semidirect |
| 35. #13133138 | C22 | semidirect |
| 36. #13133138 | C22 | semidirect |
| 37. #13133129 | C22 | semidirect |
| 38. #13133129 | C22 | semidirect |
| 39. C2×#41×C53 | C22 | semidirect |
| 42. C2×SD16×C53 | C22 | semidirect |
| 43. C2×D8×C53 | C22 | semidirect |
| 44. C2×M16×C53 | C22 | semidirect |
| 53. C2×D4×C53 | D4 | semidirect |
| 75. #11719945 | D4 | semidirect |
| 180. C2×AGL(1,ℤ/8) | D53 | semidirect |
| 190. C53 | #3012 | semidirect |
| 197. C2×#41 | C2×D53 | semidirect |
| 207. C2×SD16 | C2×D53 | semidirect |
| 209. C2×D8 | C2×D53 | semidirect |
| 210. C2×M16 | C2×D53 | semidirect |
| 252. C2×D4 | C22⋊D53 | semidirect |