Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
492 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 135 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×Q16×D53 | C2 | semidirect |
| 4. #16810882 | C2 | semidirect |
| 5. #16810881 | C2 | semidirect |
| 6. #16810880 | C2 | semidirect |
| 7. #16810879 | C2 | semidirect |
| 8. #16810878 | C2 | semidirect |
| 9. #106×D53 | C2 | semidirect |
| 10. #103×D53 | C2 | semidirect |
| 11. C53×#470 | C2 | semidirect |
| 14. C2×Dic212 | C22 | semidirect |
| 15. C2×#11719925 | C22 | semidirect |
| 31. #13133149 | C22 | semidirect |
| 32. #13133148 | C22 | semidirect |
| 33. #13133142 | C22 | semidirect |
| 34. #13133141 | C22 | semidirect |
| 35. #13133140 | C22 | semidirect |
| 36. C2×Q16×C53 | C22 | semidirect |
| 39. #106×C53 | C22 | semidirect |
| 40. #103×C53 | C22 | semidirect |
| 136. D53 | #470 | direct (N × H) |
| 145. #470 | D53 | direct (N × H) |
| 148. C53 | C2×#470 | semidirect |
| 154. C2×Q16 | C2×D53 | semidirect |
| 173. #106 | C2×D53 | semidirect |
| 177. #103 | C2×D53 | semidirect |