Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#16860800 | C2 | semidirect |
| 4. C2×#22548713 | C2 | semidirect |
| 6. #30632080 | C2 | direct (N × H) |
| 7. C2×#22548625 | C2 | semidirect |
| 8. C22×Q16×C251 | C2 | semidirect |
| 12. C2×#16860800 | C22 | semidirect |
| 19. #22548713 | C22 | semidirect |
| 25. #22548625 | C22 | semidirect |
| 29. C2×Q16×C251 | C22 | semidirect |
| 108. C2×C251 | #497 | semidirect |
| 112. C251 | C2×#497 | semidirect |
| 115. C22×Q16 | D251 | semidirect |
| 129. C2×Q16 | C2×D251 | semidirect |
| 222. C2 | #30632080 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860800 | 2 |
| C22×#16860799 | 2 |
| C22×#16860797 | 2 |
| C2×#22548713 | 2 |
| C2×#22548704 | 2 |
| #30632080 | 2 |
| C2×#22548625 | 2 |
| C22×Q16×C251 | 2 |
| C2×#497 | 251 |