Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
180 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. #14520801 | C2 | semidirect |
| 5. #14520800 | C2 | semidirect |
| 6. #14520799 | C2 | semidirect |
| 7. C31×#335 | C2 | semidirect |
| 39. #92469 | C8 | semidirect |
| 56. C8×C31 | C2×C8 | semidirect |
| 60. C31⋊C8 | C2×C8 | semidirect |
| 78. #335 | D31 | semidirect |
| 100. C31 | #1565 | semidirect |
| 138. C8 | C8×D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521101 | 2 |
| C4⋊C8×D31 | 2 |
| C4×#92469 | 2 |
| #14520801 | 2 |
| #14520800 | 2 |
| #14520799 | 2 |
| C31×#335 | 2 |
| #1565 | 31 |