Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
370 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 370 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 |
|---|---|---|
| 1. #16864197 | C2 | semidirect |
| 2. #16863832 | C2 | semidirect |
| 3. #16863830 | C2 | semidirect |
| 4. #16863828 | C2 | semidirect |
| 5. #16863825 | C2 | semidirect |
| 6. D16×D67 | C2 | semidirect |
| 7. #16863812 | C2 | semidirect |
| 8. C2×D16×C67 | C2 | semidirect |
| 12. #14524065 | C22 | semidirect |
| 13. #14524062 | C22 | semidirect |
| 14. D8×D67 | C22 | semidirect |
| 16. Dic536 | C22 | semidirect |
| 17. #14523988 | C22 | semidirect |
| 18. #14523987 | C22 | semidirect |
| 19. D1072 | C22 | semidirect |
| 20. #14523984 | C22 | semidirect |
| 21. #14523983 | C22 | semidirect |
| 22. #14523982 | C22 | semidirect |
| 23. C16×D67 | C22 | semidirect |
| 24. C2×D8×C67 | C22 | semidirect |
| 25. D16×C67 | C22 | semidirect |
| 26. D16×C67 | C22 | semidirect |
| 27. C2×C16×C67 | C22 | semidirect |
| 85. C67 | #3415 | semidirect |
| 92. C2×D16 | D67 | semidirect |
| 100. C2×D8 | C2×D67 | semidirect |
| 107. D16 | C2×D67 | semidirect |
| 108. D16 | C2×D67 | semidirect |
| 112. C2×C16 | C2×D67 | semidirect |