Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
488 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 123 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. #16811168 | C2 | semidirect |
| 2. C2×D4×Dic53 | C2 | semidirect |
| 3. #16810942 | C2 | semidirect |
| 4. #16810939 | C2 | semidirect |
| 5. #16810911 | C2 | semidirect |
| 6. #16810816 | C2 | semidirect |
| 7. #16810757 | C2 | semidirect |
| 8. #16810735 | C2 | semidirect |
| 9. #16810732 | C2 | semidirect |
| 10. #16810677 | C2 | semidirect |
| 11. C53×#447 | C2 | semidirect |
| 15. #13133216 | C22 | semidirect |
| 16. #13133213 | C22 | semidirect |
| 24. D4×Dic53 | C22 | semidirect |
| 25. #13133179 | C22 | semidirect |
| 30. #13133149 | C22 | semidirect |
| 31. #13133148 | C22 | semidirect |
| 32. #13133146 | C22 | semidirect |
| 33. #13133139 | C22 | semidirect |
| 35. #13133138 | C22 | semidirect |
| 37. #13133127 | C22 | semidirect |
| 94. D4×C53 | #41 | semidirect |
| 157. #447 | D53 | semidirect |
| 161. C53 | #3109 | semidirect |
| 249. D4 | #11719947 | semidirect |