Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
738 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 153 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×Q8×D53 | C2 | semidirect |
| 2. C2×#13133247 | C2 | semidirect |
| 4. #16810777 | C2 | semidirect |
| 5. #16810760 | C2 | semidirect |
| 6. #16810633 | C2 | semidirect |
| 7. #16810632 | C2 | semidirect |
| 8. #16810586 | C2 | semidirect |
| 9. C2×#137×C53 | C2 | semidirect |
| 19. C2×#11719925 | C22 | semidirect |
| 20. C2×#11719923 | C22 | semidirect |
| 28. #13133142 | C22 | semidirect |
| 29. #13133141 | C22 | semidirect |
| 34. C2×Q16×C53 | C22 | semidirect |
| 35. C2×SD16×C53 | C22 | semidirect |
| 42. C2×Q8×C53 | D4 | semidirect |
| 66. C2×Dic106 | D4 | semidirect |
| 127. C2×D53 | #137 | semidirect |
| 144. C2×#137 | D53 | semidirect |
| 151. C53 | #3004 | semidirect |
| 165. C2×Q16 | C2×D53 | semidirect |
| 167. C2×SD16 | C2×D53 | semidirect |
| 193. C2×Q8 | C22⋊D53 | semidirect |