Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 3. #16863736 | C2 | semidirect |
| 4. #16863735 | C2 | semidirect |
| 5. #16863730 | C2 | semidirect |
| 6. #16863725 | C2 | semidirect |
| 7. #16863438 | C2 | semidirect |
| 8. #16863432 | C2 | semidirect |
| 9. C2×#14523967 | C2 | semidirect |
| 11. #419×C67 | C2 | semidirect |
| 127. C67 | #3097 | semidirect |
| 136. #419 | D67 | semidirect |