Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
492 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 221 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. #16811101 | C2 | semidirect |
| 3. #16810724 | C2 | semidirect |
| 4. SD16×Dic53 | C2 | semidirect |
| 5. #16810661 | C2 | semidirect |
| 6. #16810632 | C2 | semidirect |
| 8. #16810578 | C2 | semidirect |
| 12. Q8×Dic53 | C22 | semidirect |
| 20. #13133151 | C22 | semidirect |
| 21. #13133149 | C22 | semidirect |
| 22. #13133141 | C22 | semidirect |
| 24. #13133127 | C22 | semidirect |
| 25. C8×Dic53 | C22 | semidirect |
| 28. C2×SD16×C53 | C4 | semidirect |
| 35. C2×Q8×C53 | C2×C4 | semidirect |
| 44. SD16×C53 | C2×C4 | semidirect |
| 45. SD16×C53 | C2×C4 | semidirect |
| 46. C2×C8×C53 | C2×C4 | semidirect |
| 113. C53 | #2949 | semidirect |
| 116. C2×SD16 | Dic53 | semidirect |
| 139. C2×Q8 | C2×Dic53 | semidirect |
| 148. SD16 | C2×Dic53 | semidirect |
| 149. SD16 | C2×Dic53 | semidirect |
| 152. C2×C8 | C2×Dic53 | semidirect |