Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 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×#13133243 | C2 | semidirect |
| 2. C2×#13133239 | C2 | semidirect |
| 3. #16811190 | C2 | semidirect |
| 4. #16811011 | C2 | semidirect |
| 5. #16811006 | C2 | semidirect |
| 6. #16810998 | C2 | semidirect |
| 7. #16810578 | C2 | semidirect |
| 8. C22×D8×C53 | C2 | semidirect |
| 12. C2×Dic212 | C22 | semidirect |
| 13. C2×#11719913 | C22 | semidirect |
| 14. C2×#11719923 | C22 | semidirect |
| 15. C2×D424 | C22 | semidirect |
| 16. C2×#11719922 | C22 | semidirect |
| 18. #13133213 | C22 | semidirect |
| 19. #13133204 | C22 | semidirect |
| 23. #13133127 | C22 | semidirect |
| 24. C8×Dic53 | C22 | semidirect |
| 45. C2×C8×C53 | D4 | semidirect |
| 54. #11719917 | D4 | semidirect |
| 104. C22×D8 | D53 | semidirect |
| 110. C53 | #3155 | semidirect |
| 154. C2×C8 | C22⋊D53 | semidirect |