Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
154 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 2. #14521172 | C2 | semidirect |
| 3. #14520871 | C2 | semidirect |
| 4. #14520862 | C2 | semidirect |
| 5. #14520858 | C2 | semidirect |
| 6. #14520827 | C2 | semidirect |
| 7. C31×#442 | C2 | semidirect |
| 15. #11758415 | C4 | semidirect |
| 16. #11758414 | C4 | semidirect |
| 32. Dic124 | C2×C4 | semidirect |
| 33. D248 | C2×C4 | semidirect |
| 38. C31⋊C16 | C2×C4 | semidirect |
| 67. #442 | D31 | semidirect |
| 89. C31 | AGL(1,ℤ/16) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521485 | 2 |
| #14521172 | 2 |
| #14520871 | 2 |
| #14520862 | 2 |
| #14520858 | 2 |
| #14520827 | 2 |
| C31×#442 | 2 |
| AGL(1,ℤ/16) | 31 |