Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
380 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 149 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. #30631442 | C2 | semidirect |
| 20. C22×C4×C251 | C8 | semidirect |
| 68. C251 | #1817 | semidirect |
| 87. C22×C4 | C251⋊C8 | 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 |
| #30631442 | 2 |
| C22×C42×C251 | 2 |
| #1817 | 251 |