Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 57 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. #14521421 | C2 | semidirect |
| 2. #14521329 | C2 | semidirect |
| 3. D4×C31⋊C8 | C2 | semidirect |
| 4. #14520799 | C2 | semidirect |
| 5. #14520794 | C2 | semidirect |
| 6. #14520793 | C2 | semidirect |
| 51. D4×C31 | SD16 | semidirect |
| 65. C31⋊C8 | D8 | semidirect |
| 108. C31 | #1665 | semidirect |
| 139. D4 | #92480 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521421 | 2 |
| #14521329 | 2 |
| D4×C31⋊C8 | 2 |
| #14520799 | 2 |
| #14520794 | 2 |
| #14520793 | 2 |
| C31×#459 | 2 |
| #1665 | 31 |