Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
396 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 123 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. #16810971 | C2 | semidirect |
| 3. #16810947 | C2 | semidirect |
| 4. #16810905 | C2 | semidirect |
| 5. #16810854 | C2 | semidirect |
| 6. #16810823 | C2 | semidirect |
| 7. #16810783 | C2 | semidirect |
| 8. C4×#11719925 | C2 | semidirect |
| 9. D4×#88322 | C2 | semidirect |
| 10. #16810617 | C2 | semidirect |
| 11. C53×#556 | C2 | semidirect |
| 128. #556 | D53 | semidirect |
| 139. C53 | #3304 | semidirect |