Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
272 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 13. #22548648 | C4 | semidirect |
| 14. #22548646 | C4 | semidirect |
| 15. #22548626 | C4 | semidirect |
| 54. C251⋊C8 | C42 | semidirect |
| 98. C251 | #1776 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548648 | 2 |
| C2×#22548646 | 2 |
| C2×#22548626 | 2 |
| C4×C4⋊Dic251 | 2 |
| #30631449 | 2 |
| C4×C4⋊C4×C251 | 2 |
| #1776 | 251 |