Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
160 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 81 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. C4⋊(C251⋊C16) | C2 | semidirect |
| 4. C16×Dic251 | C2 | semidirect |
| 5. C4⋊C16×C251 | C2 | semidirect |
| 38. C4×D251 | C16 | semidirect |
| 62. C251 | #2162 | semidirect |
| 66. C4⋊C16 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C8×D251 | 2 |
| C4⋊(C251⋊C16) | 2 |
| (C2×D251)⋊C16 | 2 |
| C16×Dic251 | 2 |
| C4⋊C16×C251 | 2 |
| #2162 | 251 |