Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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. #30632485 | C2 | semidirect |
| 2. C2×#22548741 | C2 | semidirect |
| 3. #30632453 | C2 | semidirect |
| 4. #30631954 | C2 | semidirect |
| 5. #30631947 | C2 | semidirect |
| 6. #30631736 | C2 | semidirect |
| 7. #30631671 | C2 | semidirect |
| 8. C2×#22548632 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C251 | C2 | semidirect |
| 11. #22548746 | C22 | semidirect |
| 15. #22548741 | C22 | semidirect |
| 21. #22548721 | C22 | semidirect |
| 26. #22548651 | C22 | semidirect |
| 27. #22548634 | C22 | semidirect |
| 28. #22548632 | C22 | semidirect |
| 29. #22548632 | C22 | semidirect |
| 34. C2×SD16×C251 | C22 | semidirect |
| 35. C2×D8×C251 | C22 | semidirect |
| 147. C251 | #3068 | semidirect |
| 151. C2×AGL(1,ℤ/8) | D251 | semidirect |
| 171. C2×SD16 | C2×D251 | semidirect |
| 173. C2×D8 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632485 | 2 |
| C2×#22548741 | 2 |
| #30632453 | 2 |
| #30631954 | 2 |
| #30631947 | 2 |
| #30631736 | 2 |
| #30631671 | 2 |
| C2×#22548632 | 2 |
| C2×AGL(1,ℤ/8)×C251 | 2 |
| #3068 | 251 |