Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
738 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 249 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. #41×Dic251 | C2 | semidirect |
| 3. #30631703 | C2 | semidirect |
| 4. C2×#22548641 | C2 | semidirect |
| 5. #568×C251 | C2 | semidirect |
| 7. #22548762 | C4 | semidirect |
| 8. #22548761 | C4 | semidirect |
| 14. #22548674 | C22 | semidirect |
| 15. C2×C4×Dic251 | C22 | semidirect |
| 16. #22548641 | C22 | semidirect |
| 17. #22548641 | C22 | semidirect |
| 20. C2×M16×C251 | C22 | semidirect |
| 24. #16860810 | C2×C4 | semidirect |
| 27. C2×Dic502 | C2×C4 | semidirect |
| 29. C2×D1004 | C2×C4 | semidirect |
| 83. C251 | #2901 | semidirect |
| 86. #568 | D251 | semidirect |
| 98. C2×M16 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632523 | 2 |
| #41×Dic251 | 2 |
| #30631703 | 2 |
| C2×#22548641 | 2 |
| #568×C251 | 2 |
| #2901 | 251 |