Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
468 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 468 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 |
|---|---|---|
| 2. C2×#13133176 | C2 | semidirect |
| 3. #16810948 | C2 | direct (N × H) |
| 4. C2×#13133151 | C2 | semidirect |
| 5. C2×#13133149 | C2 | semidirect |
| 6. C2×#13133139 | C2 | semidirect |
| 7. C2×#13133139 | C2 | semidirect |
| 8. C2×C22⋊C8×C53 | C2 | semidirect |
| 14. #13133176 | C22 | semidirect |
| 21. #13133151 | C22 | semidirect |
| 22. #13133149 | C22 | semidirect |
| 23. #13133139 | C22 | semidirect |
| 24. #13133139 | C22 | semidirect |
| 28. C22⋊C8×C53 | C22 | semidirect |
| 110. C2×C53 | #482 | semidirect |
| 122. C2×C22⋊C8 | D53 | semidirect |
| 123. C53 | C2×#482 | semidirect |
| 143. C22⋊C8 | C2×D53 | semidirect |
| 225. C2 | #16810948 | direct (N × H) |