Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
408 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 408 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. #16863946 | C2 | semidirect |
| 2. #16863806 | C2 | semidirect |
| 3. #16863786 | C2 | semidirect |
| 4. #16863762 | C2 | semidirect |
| 5. #16863755 | C2 | semidirect |
| 6. #16863647 | C2 | semidirect |
| 7. #16863644 | C2 | semidirect |
| 8. C4×#11761615 | C2 | semidirect |
| 9. C4×#11761613 | C2 | semidirect |
| 10. C4×#11761612 | C2 | semidirect |
| 11. #529×C67 | C2 | semidirect |
| 110. C67⋊C8 | #41 | semidirect |
| 138. C67 | #3171 | semidirect |
| 140. #529 | D67 | semidirect |