Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 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×#22548763 | C2 | semidirect |
| 2. C2×#22548741 | C2 | semidirect |
| 3. #30632254 | C2 | semidirect |
| 4. #30631831 | C2 | semidirect |
| 5. #30631824 | C2 | semidirect |
| 6. #30631696 | C2 | semidirect |
| 7. #30631684 | C2 | semidirect |
| 8. #30631653 | C2 | semidirect |
| 9. C22×SD16×C251 | C2 | semidirect |
| 13. C2×#16860811 | C22 | semidirect |
| 18. C2×Q8×D251 | C22 | semidirect |
| 28. #22548640 | C22 | semidirect |
| 29. #22548639 | C22 | semidirect |
| 30. #22548637 | C22 | semidirect |
| 31. (C2×D251)⋊C8 | C22 | semidirect |
| 44. #16860810 | D4 | semidirect |
| 72. C2×Q8×C251 | D4 | semidirect |
| 145. C251 | #3010 | semidirect |
| 149. C22×SD16 | D251 | semidirect |
| 200. C2×Q8 | C22⋊D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548763 | 2 |
| C2×#22548741 | 2 |
| #30632254 | 2 |
| #30631831 | 2 |
| #30631824 | 2 |
| #30631696 | 2 |
| #30631684 | 2 |
| #30631653 | 2 |
| C22×SD16×C251 | 2 |
| #3010 | 251 |