Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
546 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 546 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 |
|---|---|---|
| 1. C22×#11719913 | C2 | semidirect |
| 2. D4×Dic106 | C2 | semidirect |
| 4. #16810996 | C2 | semidirect |
| 5. #16810852 | C2 | semidirect |
| 6. #16810829 | C2 | semidirect |
| 7. #16810824 | C2 | semidirect |
| 8. #16810776 | C2 | semidirect |
| 9. #16810764 | C2 | semidirect |
| 10. C4×#11719913 | C2 | semidirect |
| 11. C8×D4×C53 | C2 | semidirect |
| 12. C22×Dic106 | C22 | semidirect |
| 18. C2×#11719913 | C22 | semidirect |
| 19. C2×#11719913 | C22 | semidirect |
| 20. C2×#11719913 | C22 | semidirect |
| 21. #13133217 | C22 | semidirect |
| 24. #13133196 | C22 | semidirect |
| 29. C4×Dic106 | C22 | semidirect |
| 32. #13133149 | C22 | semidirect |
| 33. #13133142 | C22 | semidirect |
| 34. #13133142 | C22 | semidirect |
| 36. #13133139 | C22 | semidirect |
| 37. C22×C8×C53 | C22 | semidirect |
| 39. C4⋊C8×C53 | C22 | semidirect |
| 40. C22⋊C8×C53 | C22 | semidirect |
| 41. C4×C8×C53 | C22 | semidirect |
| 82. #11719913 | D4 | direct (N × H) |
| 89. D4×C53 | SD16 | semidirect |
| 114. Dic106 | C2×D4 | semidirect |
| 117. C8×C53 | C2×D4 | semidirect |
| 120. C22×C53 | C2×SD16 | semidirect |
| 131. C4×C53 | C2×SD16 | semidirect |
| 155. C8×D4 | D53 | semidirect |
| 156. C53 | D4×SD16 | semidirect |
| 166. C22×C8 | C2×D53 | semidirect |
| 180. C4⋊C8 | C2×D53 | semidirect |
| 185. C22⋊C8 | C2×D53 | semidirect |
| 186. C4×C8 | C2×D53 | semidirect |
| 247. D4 | #11719913 | direct (N × H) |
| 262. C8 | D4×D53 | semidirect |
| 272. C22 | C2×#11719913 | semidirect |
| 280. C4 | C2×#11719913 | semidirect |