Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 125 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. #16863876 | C2 | semidirect |
| 3. #16863723 | C2 | semidirect |
| 4. #16863722 | C2 | semidirect |
| 5. #16863716 | C2 | semidirect |
| 6. #16863711 | C2 | semidirect |
| 7. #16863439 | C2 | semidirect |
| 8. #16863400 | C2 | semidirect |
| 9. C2×#14523965 | C2 | semidirect |
| 10. #16863362 | C2 | semidirect |
| 11. #427×C67 | C2 | semidirect |
| 23. #14524001 | C22 | semidirect |
| 25. C4⋊C4×D67 | C22 | semidirect |
| 26. #14523976 | C22 | semidirect |
| 27. #14523974 | C22 | semidirect |
| 32. (C2×D67)⋊C8 | C22 | semidirect |
| 33. (C2×D67)⋊C8 | C22 | semidirect |
| 37. #107×C67 | C22 | semidirect |
| 38. #107×C67 | C22 | semidirect |
| 39. #106×C67 | C22 | semidirect |
| 40. #106×C67 | C22 | semidirect |
| 135. C67 | #3096 | semidirect |
| 143. #427 | D67 | semidirect |
| 165. #107 | C2×D67 | semidirect |
| 166. #107 | C2×D67 | semidirect |
| 168. #106 | C2×D67 | semidirect |
| 169. #106 | C2×D67 | semidirect |