Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
374 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 117 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. #16811346 | C2 | semidirect |
| 3. #16811028 | C2 | semidirect |
| 4. #16810957 | C2 | semidirect |
| 5. #16810945 | C2 | semidirect |
| 6. #16810908 | C2 | semidirect |
| 7. #16810903 | C2 | semidirect |
| 8. #16810866 | C2 | semidirect |
| 9. #16810702 | C2 | semidirect |
| 10. #16810662 | C2 | semidirect |
| 11. C4×SD16×C53 | C2 | semidirect |
| 98. C8×C53 | #41 | semidirect |
| 131. C4×SD16 | D53 | semidirect |
| 134. C53 | #3353 | semidirect |
| 222. C8 | #11719945 | semidirect |