Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
458 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 177 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. #30632453 | C2 | semidirect |
| 3. #30631808 | C2 | semidirect |
| 4. #30631803 | C2 | semidirect |
| 5. C2×#22548641 | C2 | semidirect |
| 6. M16×Dic251 | C2 | semidirect |
| 7. #430×C251 | C2 | semidirect |
| 9. #22548748 | C4 | semidirect |
| 10. #22548743 | C4 | semidirect |
| 12. #22548723 | C22 | semidirect |
| 17. #22548641 | C22 | semidirect |
| 18. #22548641 | C22 | semidirect |
| 19. #22548625 | C22 | semidirect |
| 20. C8×Dic251 | C22 | semidirect |
| 23. #108×C251 | C22 | semidirect |
| 33. Dic1004 | C2×C4 | semidirect |
| 34. #16860799 | C2×C4 | semidirect |
| 35. D2008 | C2×C4 | semidirect |
| 85. C251 | #2956 | semidirect |
| 91. #430 | D251 | semidirect |
| 105. #108 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632487 | 2 |
| #30632453 | 2 |
| #30631808 | 2 |
| #30631803 | 2 |
| C2×#22548641 | 2 |
| M16×Dic251 | 2 |
| #430×C251 | 2 |
| #2956 | 251 |