Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
760 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 149 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×#22548748 | C2 | semidirect |
| 3. C2×#22548702 | C2 | semidirect |
| 4. #30631867 | C2 | direct (N × H) |
| 5. C2×#22548641 | C2 | semidirect |
| 6. C2×#100×C251 | C2 | semidirect |
| 12. C22×Dic502 | C22 | semidirect |
| 16. #22548748 | C22 | semidirect |
| 20. #22548702 | C22 | semidirect |
| 22. C2×C4×Dic251 | C22 | semidirect |
| 23. #22548641 | C22 | semidirect |
| 25. C2×M16×C251 | C22 | semidirect |
| 26. #100×C251 | C22 | semidirect |
| 38. C2×Dic502 | C23 | semidirect |
| 54. C4×Dic251 | C23 | semidirect |
| 62. M16×C251 | C23 | semidirect |
| 116. C2×C251 | #455 | semidirect |
| 119. C251 | C2×#455 | semidirect |
| 126. C2×#100 | D251 | semidirect |
| 140. C2×M16 | C2×D251 | semidirect |
| 146. #100 | C2×D251 | semidirect |
| 179. M16 | C22×D251 | semidirect |
| 237. C2 | #30631867 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548760 | 2 |
| C2×#22548748 | 2 |
| C2×#22548702 | 2 |
| #30631867 | 2 |
| C2×#22548641 | 2 |
| C2×#100×C251 | 2 |
| C2×#455 | 251 |