Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 2. #14521401 | C2 | semidirect |
| 3. #14521390 | C2 | semidirect |
| 4. #14521326 | C2 | semidirect |
| 5. #14521288 | C2 | semidirect |
| 6. #14521259 | C2 | semidirect |
| 7. #14521209 | C2 | semidirect |
| 8. C4×#92481 | C2 | semidirect |
| 9. D4×C31⋊C8 | C2 | semidirect |
| 10. #14521043 | C2 | semidirect |
| 11. C31×#556 | C2 | semidirect |
| 121. #556 | 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 |
|---|---|
| #14521704 | 2 |
| #14521401 | 2 |
| #14521390 | 2 |
| #14521326 | 2 |
| #14521288 | 2 |
| #14521259 | 2 |
| #14521209 | 2 |
| C4×#92481 | 2 |
| D4×C31⋊C8 | 2 |
| #14521043 | 2 |
| C31×#556 | 2 |
| #3302 | 31 |