Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
460 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 127 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×Q16×D67 | C2 | semidirect |
| 4. #16863653 | C2 | semidirect |
| 5. #16863652 | C2 | semidirect |
| 6. #16863638 | C2 | semidirect |
| 7. #16863637 | C2 | semidirect |
| 8. #16863634 | C2 | semidirect |
| 9. #16863433 | C2 | semidirect |
| 10. #16863403 | C2 | semidirect |
| 11. #467×C67 | C2 | semidirect |
| 138. C67 | #3059 | semidirect |
| 147. #467 | D67 | semidirect |