Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 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. #16811278 | C2 | semidirect |
| 2. D4×D212 | C2 | semidirect |
| 3. #16810970 | C2 | semidirect |
| 4. #16810938 | C2 | semidirect |
| 5. #16810903 | C2 | semidirect |
| 6. #16810858 | C2 | semidirect |
| 7. #16810818 | C2 | semidirect |
| 8. #16810755 | C2 | semidirect |
| 9. C8×D212 | C2 | semidirect |
| 10. #102×D53 | C2 | semidirect |
| 11. C4×D8×C53 | C2 | semidirect |
| 15. C2×#11719922 | C22 | semidirect |
| 16. C2×C8×D53 | C22 | semidirect |
| 17. #13133217 | C22 | semidirect |
| 23. #13133188 | C22 | semidirect |
| 26. C4⋊C4×D53 | C22 | semidirect |
| 27. #13133150 | C22 | semidirect |
| 28. C4⋊#88322 | C22 | semidirect |
| 29. #13133139 | C22 | semidirect |
| 30. #13133139 | C22 | semidirect |
| 32. #13133137 | C22 | semidirect |
| 33. #13133129 | C22 | semidirect |
| 36. C4×D4×C53 | C22 | semidirect |
| 37. #107×C53 | C22 | semidirect |
| 39. #102×C53 | C22 | semidirect |
| 40. C4×C8×C53 | C22 | semidirect |
| 88. D4×C53 | #41 | semidirect |
| 105. D212 | D8 | semidirect |
| 151. C4×D8 | D53 | semidirect |
| 154. C53 | #3294 | semidirect |
| 171. C4×D4 | C2×D53 | semidirect |
| 174. #107 | C2×D53 | semidirect |
| 181. #102 | C2×D53 | semidirect |
| 183. C4×C8 | C2×D53 | semidirect |
| 240. D4 | #11719945 | semidirect |