Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
340 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 115 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. #16863800 | C2 | semidirect |
| 3. #16863740 | C2 | semidirect |
| 4. #16863737 | C2 | semidirect |
| 5. #16863680 | C2 | semidirect |
| 6. #16863638 | C2 | semidirect |
| 7. #16863637 | C2 | semidirect |
| 8. #16863490 | C2 | semidirect |
| 10. #16863433 | C2 | semidirect |
| 11. #427×C67 | C2 | semidirect |
| 115. C67 | #3342 | semidirect |
| 126. #427 | D67 | semidirect |