Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
726 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 253 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×#22548722 | C2 | semidirect |
| 3. #30631695 | C2 | semidirect |
| 4. #30631686 | C2 | semidirect |
| 5. #30631681 | C2 | semidirect |
| 6. C2×#22548638 | C2 | semidirect |
| 7. #520×C251 | C2 | semidirect |
| 9. #22548762 | C4 | semidirect |
| 28. #16860810 | C2×C4 | semidirect |
| 32. C2×Dic502 | C2×C4 | semidirect |
| 94. C251 | #2898 | semidirect |
| 98. #520 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548762 | 2 |
| C2×#22548722 | 2 |
| #30631695 | 2 |
| #30631686 | 2 |
| #30631681 | 2 |
| C2×#22548638 | 2 |
| #520×C251 | 2 |
| #2898 | 251 |