Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
408 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 408 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 |
|---|---|---|
| 1. #14521720 | C2 | semidirect |
| 2. #14521397 | C2 | semidirect |
| 3. #14521373 | C2 | semidirect |
| 4. #14521341 | C2 | semidirect |
| 5. #14521283 | C2 | semidirect |
| 6. #14521244 | C2 | semidirect |
| 7. #14521192 | C2 | semidirect |
| 8. C4×#92480 | C2 | semidirect |
| 9. D4×C31⋊C8 | C2 | semidirect |
| 10. #14521043 | C2 | semidirect |
| 11. C31×#555 | C2 | semidirect |
| 127. #555 | D31 | semidirect |
| 173. C31 | #3305 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521720 | 2 |
| #14521397 | 2 |
| #14521373 | 2 |
| #14521341 | 2 |
| #14521283 | 2 |
| #14521244 | 2 |
| #14521192 | 2 |
| C4×#92480 | 2 |
| D4×C31⋊C8 | 2 |
| #14521043 | 2 |
| C31×#555 | 2 |
| #3305 | 31 |