Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
396 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 123 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. #14521397 | C2 | semidirect |
| 3. #14521373 | C2 | semidirect |
| 4. #14521331 | C2 | semidirect |
| 5. #14521280 | C2 | semidirect |
| 6. #14521249 | C2 | semidirect |
| 7. #14521209 | C2 | semidirect |
| 8. C4×#92482 | C2 | semidirect |
| 9. D4×C31⋊C8 | C2 | semidirect |
| 10. #14521043 | C2 | semidirect |
| 11. C31×#556 | C2 | semidirect |
| 123. #556 | D31 | semidirect |
| 168. C31 | #3304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521720 | 2 |
| #14521397 | 2 |
| #14521373 | 2 |
| #14521331 | 2 |
| #14521280 | 2 |
| #14521249 | 2 |
| #14521209 | 2 |
| C4×#92482 | 2 |
| D4×C31⋊C8 | 2 |
| #14521043 | 2 |
| C31×#556 | 2 |
| #3304 | 31 |