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×#14524065 | C2 | semidirect |
| 3. #16863963 | C2 | semidirect |
| 4. #16863784 | C2 | semidirect |
| 5. #16863779 | C2 | semidirect |
| 6. #16863771 | C2 | semidirect |
| 7. #16863351 | C2 | semidirect |
| 8. C22×D8×C67 | C2 | semidirect |
| 12. C2×Dic268 | C22 | semidirect |
| 13. C2×#11761617 | C22 | semidirect |
| 14. C2×#11761616 | C22 | semidirect |
| 15. C2×D536 | C22 | semidirect |
| 16. C2×#11761613 | C22 | semidirect |
| 18. #14524039 | C22 | semidirect |
| 19. #14524030 | C22 | semidirect |
| 23. #14523953 | C22 | semidirect |
| 24. C8×Dic67 | C22 | semidirect |
| 42. #11761612 | D4 | semidirect |
| 56. C2×C8×C67 | D4 | semidirect |
| 102. C67 | #3155 | semidirect |
| 105. C22×D8 | D67 | semidirect |
| 154. C2×C8 | C22⋊D67 | semidirect |