Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
162 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 61 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. #14521180 | C2 | semidirect |
| 4. #14520801 | C2 | semidirect |
| 6. #14520771 | C2 | semidirect |
| 7. C31×Q8⋊C8 | C2 | semidirect |
| 60. C31⋊C8 | M16 | semidirect |
| 78. Q8⋊C8 | D31 | semidirect |
| 100. C31 | #1592 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521180 | 2 |
| C4×#92481 | 2 |
| #14521126 | 2 |
| #14520801 | 2 |
| #14520778 | 2 |
| #14520771 | 2 |
| C31×Q8⋊C8 | 2 |
| #1592 | 31 |