Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 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 |
|---|---|---|
| 3. Q8×C31⋊C8 | C2 | semidirect |
| 4. #14520799 | C2 | semidirect |
| 5. #14520795 | C2 | semidirect |
| 7. C31×#475 | C2 | semidirect |
| 46. Q8×C31 | SD16 | semidirect |
| 62. C31⋊C8 | SD16 | semidirect |
| 77. #475 | D31 | semidirect |
| 102. C31 | #1666 | semidirect |
| 126. Q8 | #92481 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521423 | 2 |
| #14521249 | 2 |
| Q8×C31⋊C8 | 2 |
| #14520799 | 2 |
| #14520795 | 2 |
| #14520792 | 2 |
| C31×#475 | 2 |
| #1666 | 31 |