Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
446 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 2. C2×#13133248 | C2 | semidirect |
| 3. #16811390 | C2 | semidirect |
| 4. #16810896 | C2 | semidirect |
| 5. #16810888 | C2 | semidirect |
| 6. #16810671 | C2 | semidirect |
| 7. #16810605 | C2 | semidirect |
| 8. C2×#13133136 | C2 | semidirect |
| 9. C2×#137×C53 | C2 | semidirect |
| 18. C2×#11719925 | C22 | semidirect |
| 19. C2×#11719924 | C22 | semidirect |
| 26. #13133152 | C22 | semidirect |
| 27. #13133136 | C22 | semidirect |
| 28. #13133135 | C22 | semidirect |
| 29. #13133133 | C22 | semidirect |
| 145. C2×#137 | D53 | semidirect |
| 152. C53 | #3069 | semidirect |