Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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×#22548748 | C2 | semidirect |
| 3. C2×#22548703 | C2 | semidirect |
| 4. C4×#16860810 | C2 | semidirect |
| 5. #30631910 | C2 | semidirect |
| 6. #30631903 | C2 | semidirect |
| 7. #30631697 | C2 | semidirect |
| 8. #30631693 | C2 | semidirect |
| 9. #423×C251 | C2 | semidirect |
| 15. C2×Dic1004 | C22 | semidirect |
| 17. C2×#16860799 | C22 | semidirect |
| 22. C4×Dic502 | C22 | semidirect |
| 23. C4×D1004 | C22 | semidirect |
| 29. #22548640 | C22 | semidirect |
| 34. C4⋊C8×C251 | C22 | semidirect |
| 125. C251 | #3040 | semidirect |
| 133. #423 | D251 | semidirect |
| 158. C4⋊C8 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548748 | 2 |
| C2×#22548743 | 2 |
| C2×#22548703 | 2 |
| C4×#16860810 | 2 |
| #30631910 | 2 |
| #30631903 | 2 |
| #30631697 | 2 |
| #30631693 | 2 |
| #423×C251 | 2 |
| #3040 | 251 |