Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
230 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 77 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. #16863422 | C2 | semidirect |
| 5. #16863161 | C2 | semidirect |
| 6. #16863156 | C2 | semidirect |
| 7. C2×C4×C8×C67 | C2 | semidirect |
| 14. #14523968 | C4 | semidirect |
| 15. #14523965 | C4 | semidirect |
| 91. C67 | #1937 | semidirect |
| 96. C2×C4×C8 | D67 | semidirect |