Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
778 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 778 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. #30632170 | C2 | semidirect |
| 3. #30631693 | C2 | semidirect |
| 4. #30631689 | C2 | semidirect |
| 5. #30631684 | C2 | semidirect |
| 6. C2×#22548637 | C2 | semidirect |
| 7. C2×#131×C251 | C2 | semidirect |
| 9. #22548761 | C4 | semidirect |
| 16. #22548674 | C22 | semidirect |
| 17. C2×C4⋊Dic251 | C22 | semidirect |
| 18. #22548640 | C22 | semidirect |
| 19. #22548640 | C22 | semidirect |
| 20. #22548637 | C22 | semidirect |
| 21. #22548637 | C22 | semidirect |
| 22. #22548637 | C22 | semidirect |
| 25. C2×M16×C251 | C22 | semidirect |
| 26. C22×C8×C251 | C22 | semidirect |
| 30. #16860810 | C2×C4 | semidirect |
| 34. C2×D1004 | C2×C4 | semidirect |
| 97. C251 | #2897 | semidirect |
| 100. C2×#131 | D251 | semidirect |
| 114. C2×M16 | C2×D251 | semidirect |
| 115. C22×C8 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548761 | 2 |
| #30632170 | 2 |
| #30631693 | 2 |
| #30631689 | 2 |
| #30631684 | 2 |
| C2×#22548637 | 2 |
| C2×#131×C251 | 2 |
| #2897 | 251 |