Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
354 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 354 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 |
|---|---|---|
| 2. #16863703 | C2 | semidirect |
| 3. #16863678 | C2 | semidirect |
| 4. #16863673 | C2 | semidirect |
| 5. #16863635 | C2 | semidirect |
| 7. #16863618 | C2 | semidirect |
| 8. #16863603 | C2 | semidirect |
| 9. #16863598 | C2 | semidirect |
| 10. C2×C4⋊(C67⋊C8) | C2 | semidirect |
| 11. #533×C67 | C2 | semidirect |
| 134. C67 | #3248 | semidirect |
| 135. #533 | D67 | semidirect |