Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
408 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 115 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. #14521600 | C2 | semidirect |
| 2. #14521578 | C2 | semidirect |
| 3. #14521455 | C2 | semidirect |
| 4. #14521439 | C2 | semidirect |
| 5. #14521414 | C2 | semidirect |
| 6. #14521301 | C2 | semidirect |
| 7. #14521298 | C2 | semidirect |
| 8. #14521134 | C2 | semidirect |
| 9. #14521129 | C2 | semidirect |
| 10. #14521001 | C2 | semidirect |
| 11. C31×#489 | C2 | semidirect |
| 110. C31⋊C8 | #41 | semidirect |
| 137. #489 | D31 | semidirect |
| 180. C31 | #3171 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521600 | 2 |
| #14521578 | 2 |
| #14521455 | 2 |
| #14521439 | 2 |
| #14521414 | 2 |
| #14521301 | 2 |
| #14521298 | 2 |
| #14521134 | 2 |
| #14521129 | 2 |
| #14521001 | 2 |
| C31×#489 | 2 |
| #3171 | 31 |