Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
184 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 109 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. #30631462 | C2 | semidirect |
| 5. C4×C251⋊C16 | C2 | semidirect |
| 6. C16×Dic251 | C2 | semidirect |
| 7. #346×C251 | C2 | semidirect |
| 11. #22548654 | C4 | semidirect |
| 14. C16×D251 | C4 | semidirect |
| 60. C251 | #2108 | semidirect |
| 66. #346 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548654 | 2 |
| C2×C16×D251 | 2 |
| #30631641 | 2 |
| #30631462 | 2 |
| C4×C251⋊C16 | 2 |
| C16×Dic251 | 2 |
| #346×C251 | 2 |
| #2108 | 251 |