Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
304 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 4. #30631697 | C2 | semidirect |
| 5. C2×#22548633 | C2 | semidirect |
| 6. #30631458 | C2 | semidirect |
| 7. #338×C251 | C2 | semidirect |
| 12. C2×Dic1004 | C4 | semidirect |
| 13. C2×#16860799 | C4 | semidirect |
| 107. C251 | #1902 | semidirect |
| 115. #338 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548748 | 2 |
| #30632453 | 2 |
| #30631703 | 2 |
| #30631697 | 2 |
| C2×#22548633 | 2 |
| #30631458 | 2 |
| #338×C251 | 2 |
| #1902 | 251 |