Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
126 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 41 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. C22⋊(C251⋊C16) | C2 | semidirect |
| 2. #30631450 | C2 | semidirect |
| 6. C2×D8×C251 | C4 | semidirect |
| 9. #107×C251 | C4 | semidirect |
| 59. C251 | #1347 | semidirect |
| 64. C2×D8 | Dic251 | semidirect |
| 69. #107 | Dic251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22⋊(C251⋊C16) | 2 |
| #30631450 | 2 |
| #466×C251 | 2 |
| #1347 | 251 |