Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
1504 conjugacy classes of subgroups; only the 1077 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 1077 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×#22548722 | C2 | direct (N × H) |
| 2. C22×#16860794 | C2 | semidirect |
| 3. C23×C251⋊C8 | C2 | semidirect |
| 5. #22548722 | C22 | direct (N × H) |
| 6. C2×#16860794 | C22 | semidirect |
| 9. C22×C251⋊C8 | C22 | semidirect |
| 15. #16860794 | C23 | semidirect |
| 18. C2×C251⋊C8 | C23 | semidirect |
| 41. C22×C251 | #131 | semidirect |
| 48. C2×C251 | C2×#131 | semidirect |
| 50. C251 | C22×#131 | semidirect |
| 92. C22 | #22548722 | direct (N × H) |
| 99. C2 | C2×#22548722 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548722 | 2 |
| C22×#16860794 | 2 |
| C23×C251⋊C8 | 2 |
| C22×#41×C251 | 2 |
| C22×#131 | 251 |