Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
582 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 582 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. C2×#11758453 | C2 | semidirect |
| 2. #14520940 | C2 | semidirect |
| 3. #14520933 | C2 | semidirect |
| 5. #14520922 | C2 | semidirect |
| 6. #14520917 | C2 | semidirect |
| 7. C22×C42×C31 | C2 | semidirect |
| 35. C42×C31 | D4 | semidirect |
| 66. C22×C31 | #126 | semidirect |
| 79. C22×C42 | D31 | semidirect |
| 105. C31 | #2852 | semidirect |
| 123. C42 | C22⋊D31 | semidirect |
| 151. C22 | #11758453 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758453 | 2 |
| #14520940 | 2 |
| #14520933 | 2 |
| #14520928 | 2 |
| #14520922 | 2 |
| #14520917 | 2 |
| C22×C42×C31 | 2 |
| #2852 | 31 |