Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
564 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
| 3. C2×C4×D1004 | C2 | semidirect |
| 4. #30631899 | C2 | direct (N × H) |
| 5. C2×C4⋊(C251⋊C8) | C2 | semidirect |
| 6. C2×#22548639 | C2 | semidirect |
| 7. C2×#22548636 | C2 | semidirect |
| 8. C2×#124×C251 | C2 | semidirect |
| 12. C2×#16860797 | C22 | semidirect |
| 18. C4×D1004 | C22 | semidirect |
| 21. C4⋊(C251⋊C8) | C22 | semidirect |
| 22. #22548639 | C22 | semidirect |
| 23. #22548636 | C22 | semidirect |
| 27. #124×C251 | C22 | semidirect |
| 118. C2×C251 | #463 | semidirect |
| 123. C251 | C2×#463 | semidirect |
| 127. C2×#124 | D251 | semidirect |
| 144. #124 | C2×D251 | semidirect |
| 243. C2 | #30631899 | 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×C4×D1004 | 2 |
| #30631899 | 2 |
| C2×C4⋊(C251⋊C8) | 2 |
| C2×#22548639 | 2 |
| C2×#22548636 | 2 |
| C2×#124×C251 | 2 |
| C2×#463 | 251 |