Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
568 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 157 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×C4×Dic62 | C2 | semidirect |
| 3. #14520989 | C2 | semidirect |
| 4. #14520976 | C2 | semidirect |
| 6. #14520962 | C2 | semidirect |
| 7. C4×(C2×D31)⋊C4 | C2 | semidirect |
| 8. C31×#376 | C2 | semidirect |
| 99. #376 | D31 | semidirect |
| 123. C31 | #2398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic62 | 2 |
| C2×C4×D124 | 2 |
| #14520989 | 2 |
| #14520976 | 2 |
| #14520967 | 2 |
| #14520962 | 2 |
| C4×(C2×D31)⋊C4 | 2 |
| C31×#376 | 2 |
| #2398 | 31 |