Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
490 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 490 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×#22548746 | C2 | semidirect |
| 2. C22×#16860797 | C2 | semidirect |
| 4. #30631909 | C2 | semidirect |
| 5. #30631887 | C2 | semidirect |
| 6. #30631714 | C2 | semidirect |
| 7. #30631691 | C2 | semidirect |
| 8. #30631681 | C2 | semidirect |
| 9. #519×C251 | C2 | semidirect |
| 13. C2×#16860800 | C22 | semidirect |
| 16. C2×#16860797 | C22 | semidirect |
| 23. C4⋊(C251⋊C8) | C22 | semidirect |
| 24. #22548638 | C22 | semidirect |
| 26. #22548635 | C22 | semidirect |
| 29. C4×Q8×C251 | C22 | semidirect |
| 55. C2×Q8×C251 | D4 | semidirect |
| 116. C251 | #3043 | semidirect |
| 121. #519 | D251 | semidirect |
| 142. C4×Q8 | C2×D251 | semidirect |
| 156. C2×Q8 | D1004 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548746 | 2 |
| C22×#16860797 | 2 |
| #30632256 | 2 |
| #30631909 | 2 |
| #30631887 | 2 |
| #30631714 | 2 |
| #30631691 | 2 |
| #30631681 | 2 |
| #519×C251 | 2 |
| #3043 | 251 |