Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#22548706 | C2 | semidirect |
| 3. #30632054 | C2 | semidirect |
| 4. #30632050 | C2 | semidirect |
| 5. #30632043 | C2 | semidirect |
| 6. #30632040 | C2 | semidirect |
| 7. #30631689 | C2 | semidirect |
| 8. #30631688 | C2 | semidirect |
| 9. #30631686 | C2 | semidirect |
| 10. M16×Dic251 | C2 | semidirect |
| 11. #417×C251 | C2 | semidirect |
| 146. C251 | #3142 | semidirect |
| 157. #417 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632233 | 2 |
| C2×#22548706 | 2 |
| #30632054 | 2 |
| #30632050 | 2 |
| #30632043 | 2 |
| #30632040 | 2 |
| #30631689 | 2 |
| #30631688 | 2 |
| #30631686 | 2 |
| M16×Dic251 | 2 |
| #417×C251 | 2 |
| #3142 | 251 |