Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
136 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 136 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 |
| 13. #108×C251 | C4 | semidirect |
| 55. C251 | #1383 | semidirect |
| 67. #108 | Dic251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548655 | 2 |
| C2×#22548647 | 2 |
| C2×#108×C251 | 2 |
| #1383 | 251 |