Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
430 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 430 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. #16811295 | C2 | semidirect |
| 2. #16811278 | C2 | semidirect |
| 3. #16810970 | C2 | semidirect |
| 4. #16810943 | C2 | semidirect |
| 5. #16810908 | C2 | semidirect |
| 6. #16810875 | C2 | semidirect |
| 7. #16810818 | C2 | semidirect |
| 8. #16810767 | C2 | semidirect |
| 9. #16810702 | C2 | semidirect |
| 10. #16810623 | C2 | semidirect |
| 11. C4×SD16×C53 | C2 | semidirect |
| 81. Q8×C53 | #41 | semidirect |
| 143. C4×SD16 | D53 | semidirect |
| 146. C53 | #3332 | semidirect |
| 217. Q8 | #11719945 | semidirect |