Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
386 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 121 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. C2×Q8×Dic31 | C2 | semidirect |
| 3. #14521385 | C2 | semidirect |
| 5. #14521358 | C2 | semidirect |
| 6. #14521269 | C2 | semidirect |
| 7. #14521205 | C2 | semidirect |
| 8. #14521153 | C2 | semidirect |
| 9. #14521150 | C2 | semidirect |
| 10. #14521103 | C2 | semidirect |
| 174. C31 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521580 | 2 |
| C2×Q8×Dic31 | 2 |
| #14521385 | 2 |
| #14521365 | 2 |
| #14521358 | 2 |
| #14521269 | 2 |
| #14521205 | 2 |
| #14521153 | 2 |
| #14521150 | 2 |
| #14521103 | 2 |
| C31×#448 | 2 |
| #3117 | 31 |