Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
598 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 2. C22×C22⋊Dic251 | C2 | semidirect |
| 3. C2×#22548629 | C2 | semidirect |
| 4. #30631453 | C2 | semidirect |
| 5. #379×C251 | C2 | semidirect |
| 6. C22×C22⋊D251 | C4 | semidirect |
| 14. C2×C22⋊Dic251 | C4 | semidirect |
| 21. C23×D251 | C2×C4 | semidirect |
| 32. C22×Dic251 | C2×C4 | semidirect |
| 33. C22×Dic251 | C2×C4 | semidirect |
| 40. C22⋊Dic251 | D4 | semidirect |
| 108. C22×C251 | #99 | semidirect |
| 130. C251 | #1898 | semidirect |
| 135. #379 | D251 | semidirect |
| 242. C22 | #22548629 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548684 | 2 |
| C22×C22⋊Dic251 | 2 |
| C2×#22548629 | 2 |
| #30631453 | 2 |
| #379×C251 | 2 |
| #1898 | 251 |