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. #16864198 | C2 | semidirect |
| 2. #16863833 | C2 | semidirect |
| 3. #16863831 | C2 | semidirect |
| 4. #16863829 | C2 | semidirect |
| 5. C2×D1072 | C2 | semidirect |
| 6. D16×D67 | C2 | semidirect |
| 7. #16863812 | C2 | semidirect |
| 8. #508×C67 | C2 | semidirect |
| 12. #14524066 | C22 | semidirect |
| 13. C2×D536 | C22 | semidirect |
| 14. D8×D67 | C22 | semidirect |
| 16. #14523986 | C22 | semidirect |
| 17. D1072 | C22 | semidirect |
| 18. D1072 | C22 | semidirect |
| 19. #14523984 | C22 | semidirect |
| 20. #14523983 | C22 | semidirect |
| 21. #14523982 | C22 | semidirect |
| 22. C16×D67 | C22 | semidirect |
| 23. #135×C67 | C22 | semidirect |
| 24. Q32×C67 | C22 | semidirect |
| 25. SD32×C67 | C22 | semidirect |
| 26. D16×C67 | C22 | semidirect |
| 27. C2×C16×C67 | C22 | semidirect |
| 85. C67 | #3415 | semidirect |
| 90. #508 | D67 | semidirect |
| 98. #135 | C2×D67 | semidirect |
| 102. Q32 | C2×D67 | semidirect |
| 104. SD32 | C2×D67 | semidirect |
| 108. D16 | C2×D67 | semidirect |
| 112. C2×C16 | C2×D67 | semidirect |