Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
588 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 97 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. #30631705 | C2 | semidirect |
| 3. #30631703 | C2 | semidirect |
| 4. #30631692 | C2 | semidirect |
| 5. #30631669 | C2 | semidirect |
| 6. #30631660 | C2 | semidirect |
| 7. #418×C251 | C2 | semidirect |
| 15. C2×#16860809 | C4 | semidirect |
| 18. C2×D4×D251 | C4 | semidirect |
| 19. C2×#16860794 | C22 | semidirect |
| 20. #22548674 | C22 | semidirect |
| 28. C2×M16×C251 | C22 | semidirect |
| 29. #117×C251 | C22 | semidirect |
| 153. C251 | #1795 | semidirect |
| 159. #418 | D251 | semidirect |
| 175. C2×M16 | C2×D251 | semidirect |
| 177. #117 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548760 | 2 |
| #30631705 | 2 |
| #30631703 | 2 |
| #30631692 | 2 |
| #30631669 | 2 |
| #30631660 | 2 |
| #418×C251 | 2 |
| #1795 | 251 |