Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
466 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 145 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. #16864194 | C2 | semidirect |
| 2. C2×#14524071 | C2 | semidirect |
| 3. C2×#14524068 | C2 | semidirect |
| 4. #16863666 | C2 | semidirect |
| 5. #16863659 | C2 | semidirect |
| 6. #16863445 | C2 | semidirect |
| 7. #16863378 | C2 | semidirect |
| 8. C2×#14523959 | C2 | semidirect |
| 9. #568×C67 | C2 | semidirect |
| 13. #14524073 | C22 | semidirect |
| 19. #14524068 | C22 | semidirect |
| 21. C2×#11761617 | C22 | semidirect |
| 23. C2×D536 | C22 | semidirect |
| 27. #14523979 | C22 | semidirect |
| 28. #14523961 | C22 | semidirect |
| 29. #14523959 | C22 | semidirect |
| 30. #14523959 | C22 | semidirect |
| 33. #131×C67 | C22 | semidirect |
| 148. C67 | #3068 | semidirect |
| 152. #568 | D67 | semidirect |
| 175. #131 | C2×D67 | semidirect |