Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
392 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#11758447 | C2 | semidirect |
| 3. #14521418 | C2 | semidirect |
| 4. #14521414 | C2 | semidirect |
| 5. #14521404 | C2 | semidirect |
| 6. #14521051 | C2 | semidirect |
| 7. C4×M16×C31 | C2 | semidirect |
| 80. C4×M16 | D31 | semidirect |
| 102. C31 | #3142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521599 | 2 |
| C2×#11758447 | 2 |
| #14521418 | 2 |
| #14521414 | 2 |
| #14521404 | 2 |
| #14521051 | 2 |
| C4×M16×C31 | 2 |
| #3142 | 31 |