Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
544 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 205 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 |
|---|---|---|
| 2. C2×C4×Dic502 | C2 | semidirect |
| 3. #30631787 | C2 | direct (N × H) |
| 4. C2×#22548648 | C2 | semidirect |
| 5. C2×#22548638 | C2 | semidirect |
| 7. C2×#22548626 | C2 | semidirect |
| 10. C2×#16860798 | C4 | semidirect |
| 15. C4×Dic502 | C22 | semidirect |
| 19. #22548648 | C22 | semidirect |
| 20. #22548638 | C22 | semidirect |
| 22. #22548626 | C22 | semidirect |
| 32. C2×Dic502 | C2×C4 | semidirect |
| 36. #16860798 | C2×C4 | semidirect |
| 38. C2×C251⋊C8 | C2×C4 | semidirect |
| 63. Dic502 | C22×C4 | semidirect |
| 69. C251⋊C8 | C22×C4 | semidirect |
| 106. C2×C251 | #440 | semidirect |
| 110. C251 | C2×#440 | semidirect |
| 217. C2 | #30631787 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860798 | 2 |
| C2×C4×Dic502 | 2 |
| #30631787 | 2 |
| C2×#22548648 | 2 |
| C2×#22548638 | 2 |
| C2×#22548636 | 2 |
| C2×#22548626 | 2 |
| C2×C4×D4×C251 | 2 |
| C2×#440 | 251 |