Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
740 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 205 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×D124 | C2 | semidirect |
| 3. #14520952 | C2 | semidirect |
| 4. #14520950 | C2 | semidirect |
| 5. #14520928 | C2 | semidirect |
| 6. #14520925 | C2 | semidirect |
| 7. #14520914 | C2 | semidirect |
| 8. #14520895 | C2 | semidirect |
| 9. C2×C4×D4×C31 | C2 | semidirect |
| 20. #11758517 | C4 | semidirect |
| 34. C2×D4×C31 | C2×C4 | semidirect |
| 43. C2×C22⋊D31 | C2×C4 | semidirect |
| 49. C2×D124 | C2×C4 | semidirect |
| 54. C42×C31 | D4 | semidirect |
| 60. C4×Dic31 | C2×C4 | semidirect |
| 119. C2×C4×D4 | D31 | semidirect |
| 153. C31 | #2328 | semidirect |
| 164. C2×D4 | C4×D31 | semidirect |
| 184. C42 | C22⋊D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758517 | 2 |
| C2×C4×D124 | 2 |
| #14520952 | 2 |
| #14520950 | 2 |
| #14520928 | 2 |
| #14520925 | 2 |
| #14520914 | 2 |
| #14520895 | 2 |
| C2×C4×D4×C31 | 2 |
| #2328 | 31 |