Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
556 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#13133242 | C2 | semidirect |
| 2. D4×D212 | C2 | semidirect |
| 3. #16810999 | C2 | semidirect |
| 4. #16810874 | C2 | semidirect |
| 5. #16810823 | C2 | semidirect |
| 6. #16810815 | C2 | semidirect |
| 7. #16810768 | C2 | semidirect |
| 8. #16810756 | C2 | semidirect |
| 9. C4×#11719924 | C2 | semidirect |
| 10. #16810701 | C2 | semidirect |
| 11. C53×#550 | C2 | semidirect |
| 16. C2×#11719924 | C22 | semidirect |
| 18. C2×#11719922 | C22 | semidirect |
| 19. C2×#11719922 | C22 | semidirect |
| 20. C2×#11719917 | C22 | semidirect |
| 26. #13133148 | C22 | semidirect |
| 27. C4⋊#88322 | C22 | semidirect |
| 28. #13133141 | C22 | semidirect |
| 29. #13133138 | C22 | semidirect |
| 31. #13133137 | C22 | semidirect |
| 32. C22⋊#88322 | C22 | semidirect |
| 33. C4×#88322 | C22 | semidirect |
| 34. C2×#41×C53 | C22 | semidirect |
| 36. #127×C53 | C22 | semidirect |
| 38. #121×C53 | C22 | semidirect |
| 39. C4×Q8×C53 | C22 | semidirect |
| 72. #11719924 | D4 | semidirect |
| 91. Q8×C53 | C2×D4 | semidirect |
| 120. #88322 | C2×D4 | semidirect |
| 139. C4×C53 | AGL(1,ℤ/8) | semidirect |
| 152. #550 | D53 | semidirect |
| 162. C53 | #3274 | semidirect |
| 163. C2×#41 | C2×D53 | semidirect |
| 175. #127 | C2×D53 | semidirect |
| 179. #121 | C2×D53 | semidirect |
| 181. C4×Q8 | C2×D53 | semidirect |
| 242. Q8 | D4×D53 | semidirect |
| 291. C4 | #13133242 | semidirect |