Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
350 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 113 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. #14521863 | C2 | semidirect |
| 2. #14521862 | C2 | semidirect |
| 3. #14521492 | C2 | semidirect |
| 4. #14521491 | C2 | semidirect |
| 5. #14521488 | C2 | semidirect |
| 6. #14521480 | C2 | semidirect |
| 7. #14521479 | C2 | semidirect |
| 8. C2×#11758417 | C2 | semidirect |
| 9. Q32×D31 | C2 | semidirect |
| 10. #14521467 | C2 | semidirect |
| 11. C31×#510 | C2 | semidirect |
| 124. #510 | D31 | semidirect |
| 164. C31 | #3417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521863 | 2 |
| #14521862 | 2 |
| #14521492 | 2 |
| #14521491 | 2 |
| #14521488 | 2 |
| #14521480 | 2 |
| #14521479 | 2 |
| C2×#11758417 | 2 |
| Q32×D31 | 2 |
| #14521467 | 2 |
| C31×#510 | 2 |
| #3417 | 31 |