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. #30632079 | C2 | direct (N × H) |
| 5. C2×#22548626 | C2 | semidirect |
| 6. C2×C4⋊Q8×C251 | C2 | semidirect |
| 10. C2×#16860800 | C22 | semidirect |
| 17. #22548626 | C22 | semidirect |
| 20. C4⋊Q8×C251 | C22 | semidirect |
| 78. C2×C251 | #497 | semidirect |
| 82. C251 | C2×#497 | semidirect |
| 86. C2×C4⋊Q8 | D251 | semidirect |
| 99. C4⋊Q8 | C2×D251 | semidirect |
| 162. C2 | #30632079 | 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×#16860797 | 2 |
| C2×#22548703 | 2 |
| #30632079 | 2 |
| C2×#22548626 | 2 |
| C2×C4⋊Q8×C251 | 2 |
| C2×#497 | 251 |