Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
336 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 336 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 |
|---|---|---|
| 1. #14521777 | C2 | semidirect |
| 3. #14521399 | C2 | semidirect |
| 4. #14521356 | C2 | semidirect |
| 7. #14521256 | C2 | semidirect |
| 8. Q8×C31⋊C8 | C2 | semidirect |
| 9. C4×#92482 | C2 | semidirect |
| 156. C31 | #3364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521777 | 2 |
| #14521403 | 2 |
| #14521399 | 2 |
| #14521356 | 2 |
| #14521329 | 2 |
| #14521268 | 2 |
| #14521256 | 2 |
| Q8×C31⋊C8 | 2 |
| C4×#92482 | 2 |
| C4×#92480 | 2 |
| C31×#556 | 2 |
| #3364 | 31 |