Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 149 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×#22548748 | C2 | semidirect |
| 3. #30632258 | C2 | semidirect |
| 4. #30631945 | C2 | semidirect |
| 5. #30631933 | C2 | semidirect |
| 6. #30631928 | C2 | semidirect |
| 7. #30631916 | C2 | semidirect |
| 8. #30631729 | C2 | semidirect |
| 9. #30631684 | C2 | semidirect |
| 10. C2×#22548640 | C2 | semidirect |
| 11. C2×#131×C251 | C2 | semidirect |
| 79. M16×C251 | D4 | semidirect |
| 143. C251 | #3063 | semidirect |
| 146. C2×#131 | D251 | semidirect |
| 210. M16 | C22⋊D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548748 | 2 |
| #30632265 | 2 |
| #30632258 | 2 |
| #30631945 | 2 |
| #30631933 | 2 |
| #30631928 | 2 |
| #30631916 | 2 |
| #30631729 | 2 |
| #30631684 | 2 |
| C2×#22548640 | 2 |
| C2×#131×C251 | 2 |
| #3063 | 251 |