Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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×C4×Dic62 | C2 | semidirect |
| 3. #14521385 | C2 | semidirect |
| 5. #14521357 | C2 | semidirect |
| 6. #14521272 | C2 | semidirect |
| 7. #14521207 | C2 | semidirect |
| 9. #14521157 | C2 | semidirect |
| 10. #14521151 | C2 | semidirect |
| 11. C31×#432 | C2 | semidirect |
| 137. #432 | D31 | semidirect |
| 174. C31 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521583 | 2 |
| C2×C4×Dic62 | 2 |
| #14521385 | 2 |
| #14521368 | 2 |
| #14521357 | 2 |
| #14521272 | 2 |
| #14521207 | 2 |
| #14521190 | 2 |
| #14521157 | 2 |
| #14521151 | 2 |
| C31×#432 | 2 |
| #3117 | 31 |