Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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. #16811066 | C2 | semidirect |
| 3. C2×#13133162 | C2 | semidirect |
| 4. #16810898 | C2 | semidirect |
| 5. #16810437 | C2 | semidirect |
| 6. #16810431 | C2 | semidirect |
| 7. C53×#350 | C2 | semidirect |
| 14. C2×Dic212 | C22 | semidirect |
| 20. #13133153 | C22 | semidirect |
| 23. M32×C53 | C22 | semidirect |
| 24. C2×C16×C53 | C22 | semidirect |
| 98. #350 | D53 | semidirect |
| 99. C53 | #2194 | semidirect |
| 113. M32 | C2×D53 | semidirect |
| 114. C2×C16 | C2×D53 | semidirect |