Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 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. #16863949 | C2 | semidirect |
| 3. #16863763 | C2 | semidirect |
| 4. #16863759 | C2 | semidirect |
| 5. #16863757 | C2 | semidirect |
| 6. #16863754 | C2 | semidirect |
| 7. #16863393 | C2 | semidirect |
| 8. #16863392 | C2 | semidirect |
| 9. #16863390 | C2 | semidirect |
| 10. C2×#14523953 | C2 | semidirect |
| 11. #416×C67 | C2 | semidirect |
| 126. C67 | #3135 | semidirect |
| 136. #416 | D67 | semidirect |