Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
712 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13133265 | C2 | semidirect |
| 2. C2×#13133237 | C2 | semidirect |
| 3. #16811201 | C2 | semidirect |
| 4. #16810784 | C2 | semidirect |
| 5. #16810777 | C2 | semidirect |
| 6. #16810767 | C2 | semidirect |
| 7. #16810760 | C2 | semidirect |
| 8. #16810625 | C2 | semidirect |
| 9. C2×#13133141 | C2 | semidirect |
| 10. #16810591 | C2 | semidirect |
| 11. C2×#137×C53 | C2 | semidirect |
| 49. C2×Q8×C53 | D4 | semidirect |
| 71. #11719945 | D4 | semidirect |
| 171. C2×#137 | D53 | semidirect |
| 181. C53 | #3013 | semidirect |
| 233. C2×Q8 | C22⋊D53 | semidirect |