Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
226 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 226 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 |
|---|---|---|
| 7. C22⋊(C251⋊C8) | C4 | semidirect |
| 9. C251⋊#95 | C4 | semidirect |
| 12. C2×C42×C251 | C4 | semidirect |
| 75. C251 | #1284 | semidirect |
| 84. C2×C42 | Dic251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30631651 | 2 |
| #30631550 | 2 |
| C4×C22⋊C4×C251 | 2 |
| #1284 | 251 |