Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
350 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 113 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. #16864210 | C2 | semidirect |
| 2. #16864209 | C2 | semidirect |
| 3. #16863839 | C2 | semidirect |
| 4. #16863838 | C2 | semidirect |
| 5. #16863835 | C2 | semidirect |
| 6. #16863827 | C2 | semidirect |
| 7. #16863826 | C2 | semidirect |
| 8. C2×#14523989 | C2 | semidirect |
| 9. Q32×D67 | C2 | semidirect |
| 10. #16863814 | C2 | semidirect |
| 11. #510×C67 | C2 | semidirect |
| 124. C67 | #3417 | semidirect |
| 130. #510 | D67 | semidirect |