Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 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×#13133248 | C2 | semidirect |
| 2. C2×#13133243 | C2 | semidirect |
| 3. C2×#13133239 | C2 | semidirect |
| 4. #16811197 | C2 | semidirect |
| 5. #16811190 | C2 | semidirect |
| 6. #16811014 | C2 | semidirect |
| 7. #16811009 | C2 | semidirect |
| 8. #16811004 | C2 | semidirect |
| 9. #16810994 | C2 | semidirect |
| 10. #16810578 | C2 | semidirect |
| 11. C22×SD16×C53 | C2 | semidirect |
| 17. C2×Dic212 | C22 | semidirect |
| 18. C2×#11719925 | C22 | semidirect |
| 19. C2×#11719913 | C22 | semidirect |
| 20. C2×#11719913 | C22 | semidirect |
| 22. C2×#11719924 | C22 | semidirect |
| 23. C2×D424 | C22 | semidirect |
| 26. #13133215 | C22 | semidirect |
| 28. #13133206 | C22 | semidirect |
| 35. #13133127 | C22 | semidirect |
| 36. C8×Dic53 | C22 | semidirect |
| 69. C2×C8×C53 | D4 | semidirect |
| 82. #11719917 | D4 | semidirect |
| 152. C22×SD16 | D53 | semidirect |
| 160. C53 | #3154 | semidirect |
| 228. C2×C8 | C22⋊D53 | semidirect |