Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
152 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 8. #22548626 | C4 | semidirect |
| 9. C4×C251⋊C8 | C4 | semidirect |
| 55. C251 | #1288 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30631744 | 2 |
| C4×#16860794 | 2 |
| #383×C251 | 2 |
| #1288 | 251 |