Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
740 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 155 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×Q16×D53 | C2 | semidirect |
| 4. #16810781 | C2 | semidirect |
| 5. #16810780 | C2 | semidirect |
| 6. #16810779 | C2 | semidirect |
| 7. #16810778 | C2 | semidirect |
| 8. #16810777 | C2 | semidirect |
| 9. #103×D53 | C2 | semidirect |
| 11. C53×#451 | C2 | semidirect |
| 22. C2×Dic212 | C22 | semidirect |
| 23. C2×#11719925 | C22 | semidirect |
| 24. C2×#11719925 | C22 | semidirect |
| 35. #13133142 | C22 | semidirect |
| 36. #13133141 | C22 | semidirect |
| 37. #13133140 | C22 | semidirect |
| 41. C2×Q16×C53 | C22 | semidirect |
| 43. #103×C53 | C22 | semidirect |
| 100. C22×D53 | Q16 | semidirect |
| 140. C22×C53 | C2×Q16 | semidirect |
| 147. C2×D53 | C2×Q16 | semidirect |
| 165. D53 | #451 | direct (N × H) |
| 174. #451 | D53 | direct (N × H) |
| 177. C53 | C2×#451 | semidirect |
| 193. C2×Q16 | C2×D53 | semidirect |
| 207. #103 | C2×D53 | semidirect |
| 313. C22 | Q16×D53 | semidirect |