Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
228 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 228 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 |
|---|---|---|
| 4. C22×C251⋊C8 | C4 | semidirect |
| 13. C22⋊C8×C251 | C4 | semidirect |
| 18. C22⋊Dic251 | C8 | semidirect |
| 77. C251 | #1282 | semidirect |
| 90. C22⋊C8 | Dic251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊(C251⋊C8) | 2 |
| C4×C22⋊Dic251 | 2 |
| C2×C22⋊C8×C251 | 2 |
| #1282 | 251 |