Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
400 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×Dic251⋊C8 | C2 | semidirect |
| 4. #30631441 | C2 | semidirect |
| 24. C22×Dic251 | C8 | semidirect |
| 85. C22×C251 | C4⋊C8 | semidirect |
| 99. Dic251 | C22⋊C8 | semidirect |
| 108. C251 | #1797 | semidirect |
| 194. C22 | Dic251⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×Dic251 | 2 |
| C2×Dic251⋊C8 | 2 |
| C2×C22⋊(C251⋊C8) | 2 |
| #30631441 | 2 |
| C2×C22⋊C8×C251 | 2 |
| #1797 | 251 |