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. #14521580 | C2 | semidirect |
| 2. #14521450 | C2 | semidirect |
| 3. #14521432 | C2 | semidirect |
| 4. #14521402 | C2 | semidirect |
| 5. #14521290 | C2 | semidirect |
| 6. #14521276 | C2 | semidirect |
| 7. #14521143 | C2 | semidirect |
| 8. #14521140 | C2 | semidirect |
| 9. D8×Dic31 | C2 | semidirect |
| 10. C2×C8×Dic31 | C2 | semidirect |
| 157. C31 | #3168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521580 | 2 |
| #14521450 | 2 |
| #14521432 | 2 |
| #14521402 | 2 |
| #14521290 | 2 |
| #14521276 | 2 |
| #14521143 | 2 |
| #14521140 | 2 |
| D8×Dic31 | 2 |
| C2×C8×Dic31 | 2 |
| C31×#466 | 2 |
| #3168 | 31 |