Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
520 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 157 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×#22548737 | C2 | semidirect |
| 2. #30632198 | C2 | semidirect |
| 3. #30631928 | C2 | semidirect |
| 4. #30631923 | C2 | semidirect |
| 5. #30631916 | C2 | semidirect |
| 6. #30631725 | C2 | semidirect |
| 7. #30631684 | C2 | semidirect |
| 8. C23×C8×C251 | C2 | semidirect |
| 11. C2×Dic1004 | C22 | semidirect |
| 12. C2×#16860799 | C22 | semidirect |
| 13. C2×D2008 | C22 | semidirect |
| 20. #22548649 | C22 | semidirect |
| 21. #22548647 | C22 | semidirect |
| 22. #22548640 | C22 | semidirect |
| 23. #22548637 | C22 | semidirect |
| 56. C2×C8×C251 | D4 | semidirect |
| 91. C22×C251 | #135 | semidirect |
| 106. C251 | #3050 | semidirect |
| 109. C23×C8 | D251 | semidirect |
| 157. C2×C8 | C22⋊D251 | semidirect |
| 200. C22 | #22548737 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548737 | 2 |
| #30632198 | 2 |
| #30631928 | 2 |
| #30631923 | 2 |
| #30631916 | 2 |
| #30631725 | 2 |
| #30631684 | 2 |
| C23×C8×C251 | 2 |
| #3050 | 251 |