Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
166 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 5. #22548630 | C4 | semidirect |
| 7. C2×M16×C251 | C4 | semidirect |
| 8. C22×C8×C251 | C4 | semidirect |
| 53. C251 | #1391 | semidirect |
| 58. C2×M16 | Dic251 | semidirect |
| 59. C22×C8 | Dic251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30631661 | 2 |
| #408×C251 | 2 |
| #1391 | 251 |