Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
568 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 161 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. #14520988 | C2 | semidirect |
| 3. #14520975 | C2 | semidirect |
| 5. #14520960 | C2 | semidirect |
| 6. C4×(C2×D31)⋊C4 | C2 | semidirect |
| 7. #14520895 | C2 | semidirect |
| 8. C2×C4×Q8×C31 | C2 | semidirect |
| 92. C2×C4×Q8 | 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×D124 | 2 |
| #14520988 | 2 |
| #14520975 | 2 |
| #14520966 | 2 |
| #14520960 | 2 |
| C4×(C2×D31)⋊C4 | 2 |
| #14520895 | 2 |
| C2×C4×Q8×C31 | 2 |
| #2398 | 31 |