Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
490 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 125 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×#14524040 | C2 | semidirect |
| 2. #16863786 | C2 | semidirect |
| 3. #16863762 | C2 | semidirect |
| 4. #16863596 | C2 | semidirect |
| 5. #16863591 | C2 | semidirect |
| 6. #16863546 | C2 | semidirect |
| 7. #16863529 | C2 | semidirect |
| 8. #16863453 | C2 | semidirect |
| 9. #529×C67 | C2 | semidirect |
| 13. C2×#11761615 | C22 | semidirect |
| 14. C2×#11761613 | C22 | semidirect |
| 19. C4⋊(C67⋊C8) | C22 | semidirect |
| 20. #14523963 | C22 | semidirect |
| 21. #14523963 | C22 | semidirect |
| 23. #14523954 | C22 | semidirect |
| 25. #125×C67 | C22 | semidirect |
| 26. #124×C67 | C22 | semidirect |
| 30. C4×Q8×C67 | C22 | semidirect |
| 32. C4×D4×C67 | C22 | semidirect |
| 128. C67 | #3217 | semidirect |
| 130. #529 | D67 | semidirect |
| 148. #125 | C2×D67 | semidirect |
| 149. #124 | C2×D67 | semidirect |
| 153. C4×Q8 | C2×D67 | semidirect |
| 155. C4×D4 | C2×D67 | semidirect |