Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
480 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#22548713 | C2 | semidirect |
| 5. #30631896 | C2 | semidirect |
| 6. #30631891 | C2 | semidirect |
| 7. #30631710 | C2 | semidirect |
| 8. #30631695 | C2 | semidirect |
| 9. #419×C251 | C2 | semidirect |
| 116. Dic251 | #137 | semidirect |
| 121. C251 | #3039 | semidirect |
| 131. #419 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548748 | 2 |
| C2×#22548746 | 2 |
| C2×#22548713 | 2 |
| #30632155 | 2 |
| #30631896 | 2 |
| #30631891 | 2 |
| #30631710 | 2 |
| #30631695 | 2 |
| #419×C251 | 2 |
| #3039 | 251 |