Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
668 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 668 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×#16860797 | C2 | semidirect |
| 2. C22×#16860795 | C2 | semidirect |
| 3. C2×#22548712 | C2 | semidirect |
| 4. #30632077 | C2 | direct (N × H) |
| 5. C2×#22548626 | C2 | semidirect |
| 6. C2×#124×C251 | C2 | semidirect |
| 10. C2×#16860797 | C22 | semidirect |
| 12. C2×#16860795 | C22 | semidirect |
| 15. #22548712 | C22 | semidirect |
| 16. #22548626 | C22 | semidirect |
| 20. #124×C251 | C22 | semidirect |
| 32. C2×C251⋊C8 | D4 | semidirect |
| 54. C251⋊C8 | C2×D4 | semidirect |
| 84. C2×C251 | #496 | semidirect |
| 88. C251 | C2×#496 | semidirect |
| 93. C2×#124 | D251 | semidirect |
| 108. #124 | C2×D251 | semidirect |
| 174. C2 | #30632077 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860797 | 2 |
| C22×#16860795 | 2 |
| C2×#22548712 | 2 |
| #30632077 | 2 |
| C2×#22548626 | 2 |
| C2×#124×C251 | 2 |
| C2×#496 | 251 |