Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
592 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 1. C22×#92482 | C2 | semidirect |
| 2. C22×#92480 | C2 | semidirect |
| 3. C22×#92481 | C2 | semidirect |
| 5. C2×#11758452 | C2 | semidirect |
| 6. #14521431 | C2 | direct (N × H) |
| 7. C2×C4×C31⋊C8 | C2 | semidirect |
| 8. C2×C31×#124 | C2 | semidirect |
| 14. C31×#124 | C22 | semidirect |
| 18. C2×#92482 | C22 | semidirect |
| 20. C2×#92481 | C22 | semidirect |
| 22. C2×#92480 | C22 | semidirect |
| 29. #11758452 | C22 | semidirect |
| 30. C4×C31⋊C8 | C22 | semidirect |
| 117. C2×#124 | D31 | semidirect |
| 121. C2×C31 | #495 | semidirect |
| 142. #124 | C2×D31 | semidirect |
| 147. C31 | C2×#495 | semidirect |
| 230. C2 | #14521431 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92482 | 2 |
| C22×#92480 | 2 |
| C22×#92481 | 2 |
| C22×#92479 | 2 |
| C2×#11758452 | 2 |
| #14521431 | 2 |
| C2×C4×C31⋊C8 | 2 |
| C2×C31×#124 | 2 |
| C2×#495 | 31 |