Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
172 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 21. M16×C251 | C8 | semidirect |
| 56. C251 | #1278 | semidirect |
| 75. M16 | C251⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30631740 | 2 |
| C2×C4×C251⋊C8 | 2 |
| C4×M16×C251 | 2 |
| #1278 | 251 |