Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
458 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 185 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. #30632453 | C2 | semidirect |
| 3. #30631810 | C2 | semidirect |
| 4. #30631805 | C2 | semidirect |
| 5. #30631736 | C2 | semidirect |
| 6. C2×#22548643 | C2 | semidirect |
| 7. C4×M16×C251 | C2 | semidirect |
| 9. #22548748 | C4 | semidirect |
| 10. #22548743 | C4 | semidirect |
| 13. #22548721 | C22 | semidirect |
| 16. #22548651 | C22 | semidirect |
| 17. #22548643 | C22 | semidirect |
| 18. #22548643 | C22 | semidirect |
| 22. #97×C251 | C22 | semidirect |
| 23. C4×C8×C251 | C22 | semidirect |
| 32. Dic1004 | C2×C4 | semidirect |
| 33. #16860799 | C2×C4 | semidirect |
| 34. D2008 | C2×C4 | semidirect |
| 85. C251 | #2956 | semidirect |
| 93. C4×M16 | D251 | semidirect |
| 108. #97 | C2×D251 | semidirect |
| 109. C4×C8 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632487 | 2 |
| #30632453 | 2 |
| #30631810 | 2 |
| #30631805 | 2 |
| #30631736 | 2 |
| C2×#22548643 | 2 |
| C4×M16×C251 | 2 |
| #2956 | 251 |