Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
386 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 129 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. #16810958 | C2 | semidirect |
| 4. #16810930 | C2 | semidirect |
| 5. #16810845 | C2 | semidirect |
| 6. #16810779 | C2 | semidirect |
| 8. #16810728 | C2 | semidirect |
| 9. #16810721 | C2 | semidirect |
| 10. #16810680 | C2 | semidirect |
| 11. C2×C4×Q8×C53 | C2 | semidirect |
| 133. C2×C4×Q8 | D53 | semidirect |
| 143. C53 | #3117 | semidirect |