Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
620 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 141 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×D8×D67 | C2 | semidirect |
| 2. D4×C22⋊D67 | C2 | semidirect |
| 3. #16863771 | C2 | semidirect |
| 4. #16863632 | C2 | semidirect |
| 5. #16863629 | C2 | semidirect |
| 6. #16863589 | C2 | semidirect |
| 7. #16863530 | C2 | semidirect |
| 8. #16863528 | C2 | semidirect |
| 9. D8×Dic67 | C2 | semidirect |
| 10. C8×C22⋊D67 | C2 | semidirect |
| 11. C22×D8×C67 | C2 | semidirect |
| 13. C2×D4×D67 | C22 | semidirect |
| 14. C2×D536 | C22 | semidirect |
| 15. C2×#11761613 | C22 | semidirect |
| 16. C2×#11761613 | C22 | semidirect |
| 18. C2×C8×D67 | C22 | semidirect |
| 19. #14524039 | C22 | semidirect |
| 20. #14524017 | C22 | semidirect |
| 22. #14524014 | C22 | semidirect |
| 25. D4×Dic67 | C22 | semidirect |
| 27. #14523977 | C22 | semidirect |
| 28. Dic67⋊C8 | C22 | semidirect |
| 29. #14523965 | C22 | semidirect |
| 30. #14523964 | C22 | semidirect |
| 31. #14523964 | C22 | semidirect |
| 32. C22⋊(C67⋊C8) | C22 | semidirect |
| 33. (C2×D67)⋊C8 | C22 | semidirect |
| 34. C8×Dic67 | C22 | semidirect |
| 35. C22×D4×C67 | C22 | semidirect |
| 38. C2×D8×C67 | C22 | semidirect |
| 39. C2×D8×C67 | C22 | semidirect |
| 40. C22×C8×C67 | C22 | semidirect |
| 77. D8×C67 | D4 | semidirect |
| 96. D4×C67 | C2×D4 | semidirect |
| 106. C22⋊D67 | D8 | direct (N × H) |
| 117. C8×C67 | C2×D4 | semidirect |
| 129. C22×C67 | C2×D8 | semidirect |
| 137. C2×D67 | C2×D8 | semidirect |
| 144. Dic67 | C2×D8 | semidirect |
| 154. C67 | D4×D8 | semidirect |
| 156. C22×D8 | D67 | semidirect |
| 168. C22×D4 | C2×D67 | semidirect |
| 175. C2×D8 | C2×D67 | semidirect |
| 176. C2×D8 | C2×D67 | semidirect |
| 178. C22×C8 | C2×D67 | semidirect |
| 220. D8 | C22⋊D67 | direct (N × H) |
| 258. D4 | C2×C22⋊D67 | semidirect |
| 273. C8 | C2×C22⋊D67 | semidirect |
| 290. C22 | D8×D67 | semidirect |