Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
168 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 168 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 |
|---|---|---|
| 2. #14521334 | C2 | semidirect |
| 4. #14520802 | C2 | semidirect |
| 5. #14520796 | C2 | semidirect |
| 7. C31×#446 | C2 | semidirect |
| 60. C8×C31 | SD16 | semidirect |
| 79. #446 | D31 | semidirect |
| 102. C31 | #1686 | semidirect |
| 142. C8 | #92481 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521422 | 2 |
| #14521334 | 2 |
| #14521249 | 2 |
| #14520802 | 2 |
| #14520796 | 2 |
| #14520792 | 2 |
| C31×#446 | 2 |
| #1686 | 31 |