Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
512 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 213 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. #14520948 | C2 | semidirect |
| 3. #14520942 | C2 | semidirect |
| 4. #14520942 | C2 | semidirect |
| 5. #14520935 | C2 | semidirect |
| 7. #14520924 | C2 | semidirect |
| 8. #14520909 | C2 | semidirect |
| 13. C31×#123 | C4 | semidirect |
| 39. C22×C4×C31 | C2×C4 | semidirect |
| 49. C4⋊C4×C31 | C2×C4 | semidirect |
| 51. C22⋊C4×C31 | C2×C4 | semidirect |
| 139. #123 | Dic31 | semidirect |
| 158. C31 | #2376 | semidirect |
| 172. C22×C4 | C2×Dic31 | semidirect |
| 180. C4⋊C4 | C2×Dic31 | semidirect |
| 186. C22⋊C4 | C2×Dic31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14520952 | 2 |
| #14520948 | 2 |
| #14520942 | 2 |
| #14520935 | 2 |
| #14520929 | 2 |
| #14520924 | 2 |
| #14520909 | 2 |
| C2×C31×#123 | 2 |
| #2376 | 31 |