Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 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. #14521745 | C2 | semidirect |
| 2. #14521451 | C2 | semidirect |
| 3. #14521374 | C2 | semidirect |
| 4. #14521363 | C2 | semidirect |
| 5. #14521350 | C2 | semidirect |
| 6. #14521302 | C2 | semidirect |
| 7. C4×D248 | C2 | semidirect |
| 8. #14521091 | C2 | semidirect |
| 9. C31×#436 | C2 | semidirect |
| 105. #436 | D31 | semidirect |
| 137. C31 | #3355 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521745 | 2 |
| #14521451 | 2 |
| #14521374 | 2 |
| #14521363 | 2 |
| #14521350 | 2 |
| #14521302 | 2 |
| C4×D248 | 2 |
| #14521091 | 2 |
| C31×#436 | 2 |
| #3355 | 31 |