Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
332 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#11758525 | C2 | semidirect |
| 2. #14521050 | C2 | semidirect |
| 3. C2×#11758420 | C2 | semidirect |
| 4. C2×#11758421 | C2 | semidirect |
| 5. #14520817 | C2 | semidirect |
| 6. #14520813 | C2 | semidirect |
| 11. C31×AGL(1,ℤ/8) | C4 | semidirect |
| 134. AGL(1,ℤ/8) | Dic31 | semidirect |
| 151. C31 | #1907 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758525 | 2 |
| #14521050 | 2 |
| C2×#11758420 | 2 |
| C2×#11758421 | 2 |
| #14520817 | 2 |
| #14520813 | 2 |
| C2×C31×AGL(1,ℤ/8) | 2 |
| #1907 | 31 |