Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
420 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 139 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. D4×Dic106 | C2 | semidirect |
| 3. #16810974 | C2 | semidirect |
| 4. #16810954 | C2 | semidirect |
| 5. #16810909 | C2 | semidirect |
| 6. #16810852 | C2 | semidirect |
| 7. #16810829 | C2 | semidirect |
| 8. #16810764 | C2 | semidirect |
| 9. C4×#11719913 | C2 | semidirect |
| 10. C2×#13133142 | C2 | semidirect |
| 11. C8×D4×C53 | C2 | semidirect |
| 79. D4×C53 | SD16 | semidirect |
| 102. Dic106 | #41 | semidirect |
| 138. C8×D4 | D53 | semidirect |
| 140. C53 | #3298 | semidirect |
| 217. D4 | #11719913 | semidirect |