Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
390 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 2. #16863734 | C2 | semidirect |
| 3. #16863678 | C2 | semidirect |
| 4. #16863673 | C2 | semidirect |
| 5. #16863603 | C2 | semidirect |
| 6. #16863598 | C2 | semidirect |
| 8. C4×#11761618 | C2 | semidirect |
| 9. C4×#11761615 | C2 | semidirect |
| 10. #16863449 | C2 | semidirect |
| 11. #533×C67 | C2 | semidirect |
| 137. C67 | #3107 | semidirect |
| 138. #533 | D67 | semidirect |