Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
494 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 139 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. #16864050 | C2 | semidirect |
| 2. D4×D268 | C2 | semidirect |
| 3. #16863743 | C2 | semidirect |
| 4. #16863710 | C2 | semidirect |
| 5. #16863677 | C2 | semidirect |
| 6. #16863632 | C2 | semidirect |
| 7. #16863592 | C2 | semidirect |
| 8. #16863532 | C2 | semidirect |
| 9. C4×D536 | C2 | semidirect |
| 10. C2×#14523965 | C2 | semidirect |
| 11. C8×D4×C67 | C2 | semidirect |
| 16. C2×D536 | C22 | semidirect |
| 17. #14524043 | C22 | semidirect |
| 23. #14524017 | C22 | semidirect |
| 26. C4×D268 | C22 | semidirect |
| 27. C2×C4⋊Dic67 | C22 | semidirect |
| 28. #14523977 | C22 | semidirect |
| 29. #14523977 | C22 | semidirect |
| 32. #14523965 | C22 | semidirect |
| 33. #14523965 | C22 | semidirect |
| 34. #14523965 | C22 | semidirect |
| 35. #14523965 | C22 | semidirect |
| 36. C22×C8×C67 | C22 | semidirect |
| 38. C4⋊C8×C67 | C22 | semidirect |
| 39. C22⋊C8×C67 | C22 | semidirect |
| 40. C4×C8×C67 | C22 | semidirect |
| 85. D4×C67 | D8 | semidirect |
| 106. D268 | #41 | semidirect |
| 143. C67 | #3294 | semidirect |
| 153. C8×D4 | D67 | semidirect |
| 160. C22×C8 | C2×D67 | semidirect |
| 175. C4⋊C8 | C2×D67 | semidirect |
| 182. C22⋊C8 | C2×D67 | semidirect |
| 183. C4×C8 | C2×D67 | semidirect |
| 240. D4 | D536 | semidirect |