Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
234 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 4. C23×Dic251 | C4 | semidirect |
| 7. C2×C22⋊Dic251 | C4 | semidirect |
| 9. #22548630 | C4 | semidirect |
| 14. #100×C251 | C4 | semidirect |
| 102. C251 | #1390 | semidirect |
| 114. #100 | Dic251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548630 | 2 |
| #30631567 | 2 |
| C2×#100×C251 | 2 |
| #1390 | 251 |