Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 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. C2×#22548741 | C2 | semidirect |
| 3. C2×#22548737 | C2 | semidirect |
| 4. #30632261 | C2 | semidirect |
| 5. #30632254 | C2 | semidirect |
| 6. #30632078 | C2 | semidirect |
| 7. #30632073 | C2 | semidirect |
| 8. #30632068 | C2 | semidirect |
| 9. #30632058 | C2 | semidirect |
| 10. #30631642 | C2 | semidirect |
| 11. C22×SD16×C251 | C2 | semidirect |
| 17. C2×Dic1004 | C22 | semidirect |
| 18. C2×#16860800 | C22 | semidirect |
| 19. C2×#16860799 | C22 | semidirect |
| 20. C2×#16860799 | C22 | semidirect |
| 22. C2×#16860797 | C22 | semidirect |
| 23. C2×D2008 | C22 | semidirect |
| 26. #22548713 | C22 | semidirect |
| 28. #22548704 | C22 | semidirect |
| 35. #22548625 | C22 | semidirect |
| 36. C8×Dic251 | C22 | semidirect |
| 64. #16860794 | D4 | semidirect |
| 85. C2×C8×C251 | D4 | semidirect |
| 148. C251 | #3154 | semidirect |
| 153. C22×SD16 | D251 | semidirect |
| 228. C2×C8 | C22⋊D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548746 | 2 |
| C2×#22548741 | 2 |
| C2×#22548737 | 2 |
| #30632261 | 2 |
| #30632254 | 2 |
| #30632078 | 2 |
| #30632073 | 2 |
| #30632068 | 2 |
| #30632058 | 2 |
| #30631642 | 2 |
| C22×SD16×C251 | 2 |
| #3154 | 251 |