Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#14524071 | C2 | semidirect |
| 2. C2×#14524051 | C2 | semidirect |
| 3. #16863977 | C2 | semidirect |
| 4. #16863965 | C2 | semidirect |
| 5. #16863650 | C2 | semidirect |
| 6. #16863643 | C2 | semidirect |
| 7. #16863633 | C2 | semidirect |
| 8. #16863626 | C2 | semidirect |
| 9. #16863390 | C2 | semidirect |
| 10. C2×#14523963 | C2 | semidirect |
| 11. #428×C67 | C2 | semidirect |
| 19. C2×#11761611 | C22 | semidirect |
| 21. C2×C8×D67 | C22 | semidirect |
| 25. #14524023 | C22 | semidirect |
| 29. #14524018 | C22 | semidirect |
| 32. #14523966 | C22 | semidirect |
| 33. #14523966 | C22 | semidirect |
| 36. #14523963 | C22 | semidirect |
| 37. #14523963 | C22 | semidirect |
| 41. #107×C67 | C22 | semidirect |
| 42. #106×C67 | C22 | semidirect |
| 77. M16×C67 | D4 | semidirect |
| 152. C67 | #3062 | semidirect |
| 161. #428 | D67 | semidirect |
| 187. #107 | C2×D67 | semidirect |
| 188. #106 | C2×D67 | semidirect |
| 220. M16 | D268 | semidirect |