Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 157 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. C22×#11719912 | C2 | semidirect |
| 2. C2×#13133193 | C2 | semidirect |
| 4. #16810866 | C2 | direct (N × H) |
| 5. C2×#13133151 | C2 | semidirect |
| 6. C2×#13133141 | C2 | semidirect |
| 7. C2×#13133138 | C2 | semidirect |
| 8. C22×SD16×C53 | C2 | semidirect |
| 12. C2×#11719912 | C22 | semidirect |
| 15. #13133193 | C22 | semidirect |
| 23. #13133151 | C22 | semidirect |
| 24. #13133141 | C22 | semidirect |
| 25. #13133138 | C22 | semidirect |
| 29. C2×SD16×C53 | C22 | semidirect |
| 53. C2×C8×C53 | D4 | semidirect |
| 96. C8×C53 | C2×D4 | semidirect |
| 119. C2×C53 | #468 | semidirect |
| 124. C22×SD16 | D53 | semidirect |
| 132. C53 | C2×#468 | semidirect |
| 138. C2×SD16 | C2×D53 | semidirect |
| 180. C2×C8 | C22⋊D53 | semidirect |
| 221. C8 | C2×C22⋊D53 | semidirect |
| 243. C2 | #16810866 | direct (N × H) |