Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
406 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 117 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. #16864116 | C2 | semidirect |
| 2. #16864067 | C2 | semidirect |
| 3. #16863784 | C2 | semidirect |
| 4. #16863769 | C2 | semidirect |
| 5. #16863610 | C2 | semidirect |
| 6. #16863601 | C2 | semidirect |
| 7. #16863595 | C2 | semidirect |
| 8. #16863591 | C2 | semidirect |
| 9. #16863526 | C2 | semidirect |
| 10. #16863495 | C2 | semidirect |
| 11. C4×D8×C67 | C2 | semidirect |
| 105. C8×C67 | #41 | semidirect |
| 133. C67 | #3397 | semidirect |
| 144. C4×D8 | D67 | semidirect |
| 239. C8 | #11761628 | semidirect |