Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
384 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 173 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. #14521107 | C2 | semidirect |
| 3. #14521103 | C2 | semidirect |
| 4. #14521077 | C2 | semidirect |
| 5. #14521075 | C2 | semidirect |
| 7. M16×Dic31 | C2 | semidirect |
| 8. C2×#11758403 | C2 | semidirect |
| 123. C31 | #2923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×Dic31 | 2 |
| #14521107 | 2 |
| #14521103 | 2 |
| #14521077 | 2 |
| #14521075 | 2 |
| #14521016 | 2 |
| M16×Dic31 | 2 |
| C2×#11758403 | 2 |
| C31×#408 | 2 |
| #2923 | 31 |