Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
738 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 249 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. #16811390 | C2 | semidirect |
| 3. #16810641 | C2 | semidirect |
| 4. C2×#13133145 | C2 | semidirect |
| 5. C4×#41×C53 | C2 | semidirect |
| 7. #13133264 | C4 | semidirect |
| 8. #13133263 | C4 | semidirect |
| 13. C2×#11719917 | C22 | semidirect |
| 14. #13133145 | C22 | semidirect |
| 15. #13133145 | C22 | semidirect |
| 19. #117×C53 | C22 | semidirect |
| 20. C2×C42×C53 | C22 | semidirect |
| 34. #11719945 | C2×C4 | semidirect |
| 36. C2×D212 | C2×C4 | semidirect |
| 38. C2×Dic106 | C2×C4 | semidirect |
| 86. C4×#41 | D53 | semidirect |
| 89. C53 | #2901 | semidirect |
| 101. #117 | C2×D53 | semidirect |
| 102. C2×C42 | C2×D53 | semidirect |