Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
484 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#14524062 | C2 | semidirect |
| 2. #16864045 | C2 | semidirect |
| 3. #16863774 | C2 | semidirect |
| 4. #16863637 | C2 | semidirect |
| 5. #16863634 | C2 | semidirect |
| 6. #16863599 | C2 | semidirect |
| 7. #16863558 | C2 | semidirect |
| 8. #16863555 | C2 | semidirect |
| 9. D8×Dic67 | C2 | semidirect |
| 10. C8×C22⋊D67 | C2 | semidirect |
| 11. C2×#135×C67 | C2 | semidirect |
| 76. D8×C67 | D4 | semidirect |
| 129. Dic67 | #135 | semidirect |
| 137. C67 | #3283 | semidirect |
| 139. C2×#135 | D67 | semidirect |
| 198. D8 | C22⋊D67 | semidirect |