Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
544 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 197 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×Q8×Dic251 | C2 | semidirect |
| 4. #30631790 | C2 | direct (N × H) |
| 5. C2×#22548648 | C2 | semidirect |
| 7. C2×#22548625 | C2 | semidirect |
| 8. C2×#103×C251 | C2 | semidirect |
| 11. C2×#16860797 | C4 | semidirect |
| 15. Q8×Dic251 | C22 | semidirect |
| 23. #22548648 | C22 | semidirect |
| 25. #22548625 | C22 | semidirect |
| 29. #103×C251 | C22 | semidirect |
| 40. #16860797 | C2×C4 | semidirect |
| 41. C2×C251⋊C8 | C2×C4 | semidirect |
| 52. C2×Q8×C251 | C2×C4 | semidirect |
| 75. C251⋊C8 | C22×C4 | semidirect |
| 79. Q8×C251 | C22×C4 | semidirect |
| 105. C2×C251 | #440 | semidirect |
| 110. C251 | C2×#440 | semidirect |
| 117. C2×#103 | D251 | semidirect |
| 138. #103 | C2×D251 | semidirect |
| 144. C2×Q8 | C4×D251 | semidirect |
| 179. Q8 | C2×C4×D251 | semidirect |
| 217. C2 | #30631790 | 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 |
| C2×Q8×Dic251 | 2 |
| C2×#22548677 | 2 |
| #30631790 | 2 |
| C2×#22548648 | 2 |
| C2×#22548637 | 2 |
| C2×#22548625 | 2 |
| C2×#103×C251 | 2 |
| C2×#440 | 251 |