Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
544 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 544 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×#16860799 | C2 | semidirect |
| 2. C2×#22548694 | C2 | semidirect |
| 4. #30631933 | C2 | direct (N × H) |
| 5. C2×#22548649 | C2 | semidirect |
| 6. C2×#22548640 | C2 | semidirect |
| 7. C2×#22548637 | C2 | semidirect |
| 8. C22×M16×C251 | C2 | semidirect |
| 13. C2×#16860799 | C22 | semidirect |
| 15. #22548694 | C22 | semidirect |
| 23. #22548649 | C22 | semidirect |
| 24. #22548640 | C22 | semidirect |
| 25. #22548637 | C22 | semidirect |
| 28. C2×M16×C251 | C22 | semidirect |
| 62. C2×C8×C251 | D4 | semidirect |
| 97. C8×C251 | C2×D4 | semidirect |
| 118. C2×C251 | #468 | semidirect |
| 123. C251 | C2×#468 | semidirect |
| 126. C22×M16 | D251 | semidirect |
| 140. C2×M16 | C2×D251 | semidirect |
| 179. C2×C8 | C22⋊D251 | semidirect |
| 221. C8 | C2×C22⋊D251 | semidirect |
| 243. C2 | #30631933 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860799 | 2 |
| C2×#22548694 | 2 |
| C2×#22548689 | 2 |
| #30631933 | 2 |
| C2×#22548649 | 2 |
| C2×#22548640 | 2 |
| C2×#22548637 | 2 |
| C22×M16×C251 | 2 |
| C2×#468 | 251 |