Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
398 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 117 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. #14521764 | C2 | semidirect |
| 2. #14521703 | C2 | semidirect |
| 3. #14521400 | C2 | semidirect |
| 4. #14521392 | C2 | semidirect |
| 5. #14521339 | C2 | semidirect |
| 6. #14521277 | C2 | semidirect |
| 7. #14521254 | C2 | semidirect |
| 8. #14521191 | C2 | semidirect |
| 9. C8×D124 | C2 | semidirect |
| 10. #14521042 | C2 | semidirect |
| 11. C4×D8×C31 | C2 | semidirect |
| 133. C4×D8 | D31 | semidirect |
| 171. C31 | #3303 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521764 | 2 |
| #14521703 | 2 |
| #14521400 | 2 |
| #14521392 | 2 |
| #14521339 | 2 |
| #14521277 | 2 |
| #14521254 | 2 |
| #14521191 | 2 |
| C8×D124 | 2 |
| #14521042 | 2 |
| C4×D8×C31 | 2 |
| #3303 | 31 |