Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
300 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 3. #30631643 | C2 | semidirect |
| 4. C2×C8×Dic251 | C2 | semidirect |
| 5. #30631452 | C2 | semidirect |
| 6. #30631446 | C2 | semidirect |
| 9. #22548722 | C4 | semidirect |
| 16. #22548642 | C4 | semidirect |
| 23. #103×C251 | C4 | semidirect |
| 24. #102×C251 | C4 | semidirect |
| 98. C251 | #1764 | semidirect |
| 119. #103 | Dic251 | semidirect |
| 120. #102 | Dic251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548722 | 2 |
| C2×#22548642 | 2 |
| #30631643 | 2 |
| C2×C8×Dic251 | 2 |
| #30631452 | 2 |
| #30631446 | 2 |
| #416×C251 | 2 |
| #1764 | 251 |