Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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. #16864111 | C2 | semidirect |
| 2. #16864051 | C2 | semidirect |
| 3. #16863794 | C2 | semidirect |
| 4. #16863719 | C2 | semidirect |
| 5. #16863713 | C2 | semidirect |
| 6. #16863686 | C2 | semidirect |
| 7. #16863676 | C2 | semidirect |
| 8. #16863646 | C2 | semidirect |
| 9. #16863475 | C2 | semidirect |
| 10. #16863437 | C2 | semidirect |
| 11. C4×D8×C67 | C2 | semidirect |
| 100. C8×C67 | #41 | semidirect |
| 128. C67 | #3354 | semidirect |
| 137. C4×D8 | D67 | semidirect |
| 229. C8 | #11761628 | semidirect |