Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
414 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 113 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×#14524019 | C2 | semidirect |
| 3. #16863735 | C2 | semidirect |
| 4. #16863729 | C2 | semidirect |
| 5. #16863715 | C2 | semidirect |
| 6. #16863651 | C2 | semidirect |
| 7. #16863645 | C2 | semidirect |
| 8. #16863557 | C2 | semidirect |
| 9. #16863535 | C2 | semidirect |
| 10. #16863358 | C2 | semidirect |
| 11. #451×C67 | C2 | semidirect |
| 14. C2×#11761615 | C22 | semidirect |
| 31. #14523976 | C22 | semidirect |
| 32. #14523975 | C22 | semidirect |
| 33. #14523967 | C22 | semidirect |
| 34. #14523967 | C22 | semidirect |
| 35. #14523965 | C22 | semidirect |
| 39. C2×Q16×C67 | C22 | semidirect |
| 41. #103×C67 | C22 | semidirect |
| 150. C67 | #3196 | semidirect |
| 159. #451 | D67 | semidirect |
| 165. C2×Q16 | C2×D67 | semidirect |
| 188. #103 | C2×D67 | semidirect |