Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
364 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 129 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. #14521606 | C2 | semidirect |
| 3. #14521458 | C2 | semidirect |
| 4. #14521443 | C2 | semidirect |
| 5. #14521418 | C2 | semidirect |
| 6. #14521409 | C2 | semidirect |
| 7. #14521307 | C2 | semidirect |
| 9. C4×Dic124 | C2 | semidirect |
| 10. C4×#92470 | C2 | semidirect |
| 11. C4×M16×C31 | C2 | semidirect |
| 135. C4×M16 | D31 | semidirect |
| 172. C31 | #3172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521606 | 2 |
| #14521583 | 2 |
| #14521458 | 2 |
| #14521443 | 2 |
| #14521418 | 2 |
| #14521409 | 2 |
| #14521307 | 2 |
| #14521295 | 2 |
| C4×Dic124 | 2 |
| C4×#92470 | 2 |
| C4×M16×C31 | 2 |
| #3172 | 31 |