Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
348 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 125 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. #14521406 | C2 | semidirect |
| 4. #14521346 | C2 | semidirect |
| 5. #14521331 | C2 | semidirect |
| 6. #14521271 | C2 | semidirect |
| 8. Q8×C31⋊C8 | C2 | semidirect |
| 9. C4×#92482 | C2 | semidirect |
| 10. C4×#92481 | C2 | semidirect |
| 11. C31×#557 | C2 | semidirect |
| 115. #557 | D31 | semidirect |
| 158. C31 | #3365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521784 | 2 |
| #14521406 | 2 |
| #14521397 | 2 |
| #14521346 | 2 |
| #14521331 | 2 |
| #14521271 | 2 |
| #14521249 | 2 |
| Q8×C31⋊C8 | 2 |
| C4×#92482 | 2 |
| C4×#92481 | 2 |
| C31×#557 | 2 |
| #3365 | 31 |