Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
132 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 73 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. C2×C251⋊C16 | C4 | semidirect |
| 9. #22548651 | C4 | semidirect |
| 54. C251 | #1382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C251⋊C16 | 2 |
| C2×#22548651 | 2 |
| #427×C251 | 2 |
| #1382 | 251 |