Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
738 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 153 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. C22×Q8×D53 | C2 | semidirect |
| 2. C2×#13133250 | C2 | semidirect |
| 3. C2×#13133248 | C2 | semidirect |
| 5. #16810780 | C2 | semidirect |
| 6. #16810763 | C2 | semidirect |
| 7. #16810631 | C2 | semidirect |
| 8. #16810586 | C2 | semidirect |
| 9. C53×#419 | C2 | semidirect |
| 21. C2×Dic212 | C22 | semidirect |
| 22. C2×#11719925 | C22 | semidirect |
| 23. C2×#11719913 | C22 | semidirect |
| 24. C2×#11719924 | C22 | semidirect |
| 31. #13133140 | C22 | semidirect |
| 36. #103×C53 | C22 | semidirect |
| 40. C2×Q8×C53 | D4 | semidirect |
| 65. C2×Dic106 | D4 | semidirect |
| 127. C2×D53 | #137 | semidirect |
| 149. #419 | D53 | semidirect |
| 151. C53 | #3004 | semidirect |
| 177. #103 | C2×D53 | semidirect |
| 194. C2×Q8 | D212 | semidirect |