Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
856 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 269 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. C22×C4×Dic251 | C2 | semidirect |
| 3. C2×#22548641 | C2 | direct (N × H) |
| 4. C22×M16×C251 | C2 | semidirect |
| 7. C2×#16860810 | C4 | semidirect |
| 9. C22×Dic502 | C4 | semidirect |
| 10. C22×D1004 | C4 | semidirect |
| 15. C2×C4×Dic251 | C22 | semidirect |
| 16. #22548641 | C22 | direct (N × H) |
| 19. C2×M16×C251 | C22 | semidirect |
| 25. #16860810 | C2×C4 | semidirect |
| 28. C2×Dic502 | C2×C4 | semidirect |
| 30. C2×D1004 | C2×C4 | semidirect |
| 39. C4×Dic251 | C23 | semidirect |
| 48. M16×C251 | C23 | semidirect |
| 53. Dic502 | C22×C4 | semidirect |
| 55. D1004 | C22×C4 | semidirect |
| 79. C22×C251 | #104 | semidirect |
| 93. C2×C251 | C2×#104 | semidirect |
| 96. C251 | C22×#104 | semidirect |
| 99. C22×M16 | D251 | semidirect |
| 113. C2×M16 | C2×D251 | semidirect |
| 143. M16 | C22×D251 | semidirect |
| 178. C22 | #22548641 | direct (N × H) |
| 191. C2 | C2×#22548641 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860810 | 2 |
| C22×C4×Dic251 | 2 |
| C2×#22548641 | 2 |
| C22×M16×C251 | 2 |
| C22×#104 | 251 |