Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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. #16863953 | C2 | semidirect |
| 3. #16863756 | C2 | semidirect |
| 4. #16863751 | C2 | semidirect |
| 5. #16863406 | C2 | semidirect |
| 7. C4×M16×C67 | C2 | semidirect |
| 10. #14524043 | C22 | semidirect |
| 11. #14524035 | C22 | semidirect |
| 19. #14523968 | C22 | semidirect |
| 23. #97×C67 | C22 | semidirect |
| 24. C4×C8×C67 | C22 | semidirect |
| 84. C67 | #3140 | semidirect |
| 91. C4×M16 | D67 | semidirect |
| 107. #97 | C2×D67 | semidirect |
| 108. C4×C8 | C2×D67 | semidirect |