Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
800 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 209 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. #16811097 | C2 | semidirect |
| 3. #16810597 | C2 | semidirect |
| 4. #16810596 | C2 | semidirect |
| 5. #99×D53 | C2 | semidirect |
| 6. C53×#410 | C2 | semidirect |
| 9. C2×#11719949 | C4 | semidirect |
| 10. C2×#11719945 | C4 | semidirect |
| 12. C22×D212 | C4 | semidirect |
| 14. C2×D4×D53 | C4 | semidirect |
| 18. #13133176 | C22 | semidirect |
| 19. C22⋊C4×D53 | C22 | semidirect |
| 20. #13133132 | C22 | semidirect |
| 21. #13133131 | C22 | semidirect |
| 23. #117×C53 | C22 | semidirect |
| 24. #99×C53 | C22 | semidirect |
| 25. C23×D53 | C2×C4 | semidirect |
| 29. C2×Q8×C53 | C2×C4 | semidirect |
| 30. C2×D4×C53 | C2×C4 | semidirect |
| 32. C22×C4×C53 | C2×C4 | semidirect |
| 34. C2×C22⋊D53 | C2×C4 | semidirect |
| 47. C2×D212 | C2×C4 | semidirect |
| 48. C2×D212 | C2×C4 | semidirect |
| 52. C2×C4×D53 | C2×C4 | semidirect |
| 53. C2×C4×D53 | C2×C4 | semidirect |
| 54. C2×Dic106 | C2×C4 | semidirect |
| 125. #410 | D53 | semidirect |
| 127. C53 | #2883 | semidirect |
| 141. #117 | C2×D53 | semidirect |
| 145. #99 | C2×D53 | semidirect |
| 156. C2×Q8 | C4×D53 | semidirect |
| 169. C2×D4 | C4×D53 | semidirect |
| 174. C22×C4 | C4×D53 | semidirect |