Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
812 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 165 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×#11719949 | C2 | semidirect |
| 2. C22×#11719924 | C2 | semidirect |
| 3. C22×D424 | C2 | semidirect |
| 4. C2×#13133192 | C2 | semidirect |
| 5. #16810771 | C2 | direct (N × H) |
| 6. C2×#13133137 | C2 | semidirect |
| 7. C2×#13133129 | C2 | semidirect |
| 8. C2×#103×C53 | C2 | semidirect |
| 12. C2×#11719949 | C22 | semidirect |
| 20. C2×#11719924 | C22 | semidirect |
| 22. C2×D424 | C22 | semidirect |
| 25. #13133192 | C22 | semidirect |
| 27. #13133137 | C22 | semidirect |
| 28. #13133129 | C22 | semidirect |
| 32. #103×C53 | C22 | semidirect |
| 38. C2×Q8×C53 | D4 | semidirect |
| 56. C2×D212 | D4 | semidirect |
| 89. Q8×C53 | C2×D4 | semidirect |
| 107. D212 | C2×D4 | semidirect |
| 137. C2×C53 | #449 | semidirect |
| 149. C2×#103 | D53 | semidirect |
| 152. C53 | C2×#449 | semidirect |
| 174. #103 | C2×D53 | semidirect |
| 185. C2×Q8 | D212 | semidirect |
| 233. Q8 | C2×D212 | semidirect |
| 283. C2 | #16810771 | direct (N × H) |