Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
190 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 68. C251 | #1298 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30631651 | 2 |
| C2×C22⋊(C251⋊C8) | 2 |
| C2×C22⋊C8×C251 | 2 |
| #1298 | 251 |