Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
414 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 121 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×#14524022 | C2 | semidirect |
| 2. #16863737 | C2 | semidirect |
| 3. #16863729 | C2 | semidirect |
| 4. #16863712 | C2 | semidirect |
| 5. #16863652 | C2 | semidirect |
| 6. #16863640 | C2 | semidirect |
| 7. #16863558 | C2 | semidirect |
| 8. #16863551 | C2 | semidirect |
| 9. #16863534 | C2 | semidirect |
| 10. #16863360 | C2 | semidirect |
| 13. C2×#11761618 | C22 | semidirect |
| 14. C2×#11761616 | C22 | semidirect |
| 23. #14523976 | C22 | semidirect |
| 24. #14523974 | C22 | semidirect |
| 25. #14523967 | C22 | semidirect |
| 26. #14523966 | C22 | semidirect |
| 27. #14523966 | C22 | semidirect |
| 28. #14523964 | C22 | semidirect |
| 150. C67 | #3196 | semidirect |