Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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. #14521772 | C2 | semidirect |
| 3. #14521400 | C2 | semidirect |
| 4. #14521393 | C2 | semidirect |
| 5. #14521329 | C2 | semidirect |
| 6. #14521289 | C2 | semidirect |
| 7. #14521259 | C2 | semidirect |
| 8. #14521208 | C2 | semidirect |
| 9. C8×D124 | C2 | semidirect |
| 10. #14521042 | C2 | semidirect |
| 11. C4×SD16×C31 | C2 | semidirect |
| 129. C4×SD16 | D31 | semidirect |
| 166. C31 | #3302 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521772 | 2 |
| #14521703 | 2 |
| #14521400 | 2 |
| #14521393 | 2 |
| #14521329 | 2 |
| #14521289 | 2 |
| #14521259 | 2 |
| #14521208 | 2 |
| C8×D124 | 2 |
| #14521042 | 2 |
| C4×SD16×C31 | 2 |
| #3302 | 31 |