Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
364 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 364 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. C2×#14524062 | C2 | semidirect |
| 2. #135×D67 | C2 | semidirect |
| 3. #16863839 | C2 | semidirect |
| 4. #16863836 | C2 | semidirect |
| 5. #16863835 | C2 | semidirect |
| 6. #16863832 | C2 | semidirect |
| 7. #16863830 | C2 | semidirect |
| 8. #16863827 | C2 | semidirect |
| 9. #16863825 | C2 | semidirect |
| 10. M32×D67 | C2 | semidirect |
| 11. #509×C67 | C2 | semidirect |
| 14. #14524066 | C22 | semidirect |
| 21. #14524062 | C22 | semidirect |
| 22. #14524062 | C22 | semidirect |
| 23. C2×Dic268 | C22 | semidirect |
| 24. Q16×D67 | C22 | semidirect |
| 27. D8×D67 | C22 | semidirect |
| 29. Dic536 | C22 | semidirect |
| 30. #14523989 | C22 | semidirect |
| 31. #14523988 | C22 | semidirect |
| 32. #14523987 | C22 | semidirect |
| 33. #14523987 | C22 | semidirect |
| 34. #14523984 | C22 | semidirect |
| 35. #14523983 | C22 | semidirect |
| 36. #14523982 | C22 | semidirect |
| 37. C16×D67 | C22 | semidirect |
| 39. C2×D8×C67 | C22 | semidirect |
| 40. SD32×C67 | C22 | semidirect |
| 41. D16×C67 | C22 | semidirect |
| 42. M32×C67 | C22 | semidirect |
| 147. C67 | #3414 | semidirect |
| 155. #509 | D67 | semidirect |
| 176. C2×D8 | C2×D67 | semidirect |
| 183. SD32 | C2×D67 | semidirect |
| 185. D16 | C2×D67 | semidirect |
| 188. M32 | C2×D67 | semidirect |