Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
728 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 149 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×#22548762 | C2 | semidirect |
| 2. C2×#22548741 | C2 | semidirect |
| 3. C2×#22548702 | C2 | semidirect |
| 4. #30631858 | C2 | direct (N × H) |
| 5. C2×#22548642 | C2 | semidirect |
| 6. C2×#22548641 | C2 | semidirect |
| 7. C2×#22548633 | C2 | semidirect |
| 8. C2×AGL(1,ℤ/8)×C251 | C2 | semidirect |
| 12. #22548762 | C22 | semidirect |
| 21. #22548741 | C22 | semidirect |
| 26. #22548702 | C22 | semidirect |
| 29. #22548642 | C22 | semidirect |
| 30. #22548641 | C22 | semidirect |
| 31. #22548633 | C22 | semidirect |
| 35. AGL(1,ℤ/8)×C251 | C22 | semidirect |
| 172. C2×C251 | #454 | semidirect |
| 175. C251 | C2×#454 | semidirect |
| 179. C2×AGL(1,ℤ/8) | D251 | semidirect |
| 201. AGL(1,ℤ/8) | C2×D251 | semidirect |
| 349. C2 | #30631858 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548762 | 2 |
| C2×#22548741 | 2 |
| C2×#22548702 | 2 |
| #30631858 | 2 |
| C2×#22548642 | 2 |
| C2×#22548641 | 2 |
| C2×#22548633 | 2 |
| C2×AGL(1,ℤ/8)×C251 | 2 |
| C2×#454 | 251 |