Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14524068 | C2 | semidirect |
| 2. C2×#14524049 | C2 | semidirect |
| 3. #16863974 | C2 | semidirect |
| 4. #16863965 | C2 | semidirect |
| 5. #16863648 | C2 | semidirect |
| 6. #16863645 | C2 | semidirect |
| 7. #16863631 | C2 | semidirect |
| 8. #16863628 | C2 | semidirect |
| 9. #16863439 | C2 | semidirect |
| 10. C2×#14523965 | C2 | semidirect |
| 11. #416×C67 | C2 | semidirect |
| 19. C2×#11761611 | C22 | semidirect |
| 20. C2×C8×D67 | C22 | semidirect |
| 24. #14524019 | C22 | semidirect |
| 29. #14524014 | C22 | semidirect |
| 32. #14523976 | C22 | semidirect |
| 33. #14523974 | C22 | semidirect |
| 39. #103×C67 | C22 | semidirect |
| 40. #103×C67 | C22 | semidirect |
| 41. #102×C67 | C22 | semidirect |
| 42. #102×C67 | C22 | semidirect |
| 60. #11761612 | D4 | semidirect |
| 152. C67 | #3062 | semidirect |
| 162. #416 | D67 | semidirect |
| 189. #103 | C2×D67 | semidirect |
| 190. #103 | C2×D67 | semidirect |
| 193. #102 | C2×D67 | semidirect |
| 194. #102 | C2×D67 | semidirect |