Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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×#13133225 | C2 | semidirect |
| 3. #16811197 | C2 | semidirect |
| 4. #16810878 | C2 | semidirect |
| 5. #16810866 | C2 | semidirect |
| 6. #16810861 | C2 | semidirect |
| 7. #16810849 | C2 | semidirect |
| 8. #16810665 | C2 | semidirect |
| 9. #16810619 | C2 | semidirect |
| 10. C2×#13133141 | C2 | semidirect |
| 11. C2×#137×C53 | C2 | semidirect |
| 65. M16×C53 | D4 | semidirect |
| 144. C2×#137 | D53 | semidirect |
| 155. C53 | #3063 | semidirect |
| 210. M16 | C22⋊D53 | semidirect |