Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
420 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 2. C2×#13133193 | C2 | semidirect |
| 3. #16810963 | C2 | semidirect |
| 4. #16810951 | C2 | semidirect |
| 5. #16810937 | C2 | semidirect |
| 6. #16810861 | C2 | semidirect |
| 7. #16810855 | C2 | semidirect |
| 8. #16810784 | C2 | semidirect |
| 9. #16810762 | C2 | semidirect |
| 10. C22⋊C8×D53 | C2 | semidirect |
| 11. C53×#451 | C2 | semidirect |
| 14. C2×#11719924 | C22 | semidirect |
| 31. #13133151 | C22 | semidirect |
| 32. #13133148 | C22 | semidirect |
| 33. #13133141 | C22 | semidirect |
| 34. #13133141 | C22 | semidirect |
| 35. #13133139 | C22 | semidirect |
| 39. C2×Q16×C53 | C22 | semidirect |
| 41. #103×C53 | C22 | semidirect |
| 158. #451 | D53 | semidirect |
| 161. C53 | #3190 | semidirect |
| 165. C2×Q16 | C2×D53 | semidirect |
| 188. #103 | C2×D53 | semidirect |