Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
348 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 149 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. #14521457 | C2 | semidirect |
| 4. #14521456 | C2 | semidirect |
| 5. #14521450 | C2 | semidirect |
| 6. #14521449 | C2 | semidirect |
| 50. M16×C31 | Q8 | semidirect |
| 78. #92474 | Q8 | semidirect |
| 167. C31 | #3166 | semidirect |
| 176. M16 | Dic62 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521602 | 2 |
| C2×#11758467 | 2 |
| #14521457 | 2 |
| #14521456 | 2 |
| #14521450 | 2 |
| #14521449 | 2 |
| #14521092 | 2 |
| #14521091 | 2 |
| #14521089 | 2 |
| M16×Dic31 | 2 |
| C31×#428 | 2 |
| #3166 | 31 |