Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #14521586 | C2 | semidirect |
| 2. #14521450 | C2 | semidirect |
| 3. #14521434 | C2 | semidirect |
| 4. #14521405 | C2 | semidirect |
| 5. #14521287 | C2 | semidirect |
| 7. #14521281 | C2 | semidirect |
| 8. C4×#92481 | C2 | semidirect |
| 9. C4×D248 | C2 | semidirect |
| 10. C4×C8×D31 | C2 | semidirect |
| 11. C4×Q16×C31 | C2 | semidirect |
| 121. C4×Q16 | D31 | semidirect |
| 157. C31 | #3168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521586 | 2 |
| #14521450 | 2 |
| #14521434 | 2 |
| #14521405 | 2 |
| #14521287 | 2 |
| #14521286 | 2 |
| #14521281 | 2 |
| C4×#92481 | 2 |
| C4×D248 | 2 |
| C4×C8×D31 | 2 |
| C4×Q16×C31 | 2 |
| #3168 | 31 |