Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
288 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 288 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 |
|---|---|---|
| 3. #30631423 | C2 | semidirect |
| 5. C22×Dic502 | C4 | semidirect |
| 9. #22548694 | C4 | semidirect |
| 11. C2×C4⋊Dic251 | C4 | semidirect |
| 98. C251 | #1520 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548694 | 2 |
| C2×C22⋊(C251⋊C8) | 2 |
| #30631423 | 2 |
| #380×C251 | 2 |
| #1520 | 251 |