Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14524069 | C2 | semidirect |
| 2. C2×#14524068 | C2 | semidirect |
| 3. C2×#14524063 | C2 | semidirect |
| 4. C22×#11761613 | C2 | semidirect |
| 5. #16863965 | C2 | semidirect |
| 6. #16863786 | C2 | semidirect |
| 7. #16863783 | C2 | semidirect |
| 8. #16863778 | C2 | semidirect |
| 9. #16863772 | C2 | semidirect |
| 10. #16863352 | C2 | semidirect |
| 11. #535×C67 | C2 | semidirect |
| 17. C2×#11761618 | C22 | semidirect |
| 18. C2×#11761616 | C22 | semidirect |
| 19. C2×#11761616 | C22 | semidirect |
| 20. C2×#11761615 | C22 | semidirect |
| 21. C2×#11761615 | C22 | semidirect |
| 25. C2×#11761613 | C22 | semidirect |
| 26. C2×#11761613 | C22 | semidirect |
| 27. C2×#11761613 | C22 | semidirect |
| 30. #14524040 | C22 | semidirect |
| 31. #14524031 | C22 | semidirect |
| 34. #14523954 | C22 | semidirect |
| 35. C4×C67⋊C8 | C22 | semidirect |
| 38. #127×C67 | C22 | semidirect |
| 39. #124×C67 | C22 | semidirect |
| 65. #11761612 | D4 | semidirect |
| 66. C2×C67⋊C8 | D4 | semidirect |
| 154. C67 | #3155 | semidirect |
| 160. #535 | D67 | semidirect |
| 187. #127 | C2×D67 | semidirect |
| 189. #124 | C2×D67 | semidirect |