Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
388 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 139 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. #16863748 | C2 | semidirect |
| 3. #16863731 | C2 | semidirect |
| 4. #16863688 | C2 | semidirect |
| 5. #16863635 | C2 | semidirect |
| 6. #16863606 | C2 | semidirect |
| 7. #16863551 | C2 | semidirect |
| 8. C4×#11761618 | C2 | semidirect |
| 10. C2×#14523966 | C2 | semidirect |
| 80. D4×C67 | Q16 | semidirect |
| 123. C67 | #3299 | semidirect |
| 208. D4 | #11761618 | semidirect |