Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 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. C22×#11761613 | C2 | semidirect |
| 2. #16863960 | C2 | semidirect |
| 3. #16863871 | C2 | semidirect |
| 4. #16863613 | C2 | semidirect |
| 5. #16863589 | C2 | semidirect |
| 6. #16863424 | C2 | semidirect |
| 7. #16863402 | C2 | semidirect |
| 8. #16863392 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C67 | C2 | semidirect |
| 14. #14524039 | C22 | semidirect |
| 15. #14524032 | C22 | semidirect |
| 19. D4×Dic67 | C22 | semidirect |
| 23. Dic67⋊C8 | C22 | semidirect |
| 24. #14523967 | C22 | semidirect |
| 25. #14523965 | C22 | semidirect |
| 26. #14523964 | C22 | semidirect |
| 30. C2×SD16×C67 | C22 | semidirect |
| 31. C2×D8×C67 | C22 | semidirect |
| 58. C2×D4×C67 | D4 | semidirect |
| 122. C67 | #3041 | semidirect |
| 123. C2×AGL(1,ℤ/8) | D67 | semidirect |
| 136. C2×SD16 | C2×D67 | semidirect |
| 139. C2×D8 | C2×D67 | semidirect |
| 168. C2×D4 | C22⋊D67 | semidirect |