Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
1008 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 309 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×#16860794 | C2 | semidirect |
| 2. C2×#22548674 | C2 | semidirect |
| 3. #30631692 | C2 | direct (N × H) |
| 4. C2×#22548636 | C2 | semidirect |
| 7. C2×#16860794 | C22 | semidirect |
| 8. C22×C251⋊C8 | C22 | semidirect |
| 10. #22548674 | C22 | semidirect |
| 11. C2×C4⋊Dic251 | C22 | semidirect |
| 14. #22548636 | C22 | semidirect |
| 19. C22×D4×C251 | C4 | semidirect |
| 26. C2×C251⋊C8 | C23 | semidirect |
| 28. C4⋊Dic251 | C23 | semidirect |
| 43. C2×D4×C251 | C2×C4 | semidirect |
| 94. C2×C251 | #418 | semidirect |
| 97. C251 | C2×#418 | semidirect |
| 108. C22×D4 | Dic251 | semidirect |
| 133. C2×D4 | C2×Dic251 | semidirect |
| 192. C2 | #30631692 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860794 | 2 |
| C2×#22548674 | 2 |
| #30631692 | 2 |
| C2×#22548636 | 2 |
| C23×D4×C251 | 2 |
| C2×#418 | 251 |