Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
504 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 1. C2×#22548737 | C2 | semidirect |
| 2. C2×#22548734 | C2 | semidirect |
| 3. #30632355 | C2 | semidirect |
| 4. #30632062 | C2 | semidirect |
| 5. #30631924 | C2 | semidirect |
| 6. #30631886 | C2 | semidirect |
| 7. #30631833 | C2 | semidirect |
| 8. #30631830 | C2 | semidirect |
| 9. #30631781 | C2 | semidirect |
| 10. C8×C22⋊D251 | C2 | semidirect |
| 11. #466×C251 | C2 | semidirect |
| 56. Dic1004 | D4 | semidirect |
| 134. Dic251 | #135 | semidirect |
| 142. C251 | #3287 | semidirect |
| 149. #466 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548737 | 2 |
| C2×#22548734 | 2 |
| #30632355 | 2 |
| #30632062 | 2 |
| #30631924 | 2 |
| #30631886 | 2 |
| #30631833 | 2 |
| #30631830 | 2 |
| #30631781 | 2 |
| C8×C22⋊D251 | 2 |
| #466×C251 | 2 |
| #3287 | 251 |