Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
360 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 87 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. #30631710 | C2 | semidirect |
| 3. C2×#22548643 | C2 | semidirect |
| 4. C2×#22548642 | C2 | semidirect |
| 5. C2×#22548641 | C2 | semidirect |
| 6. C42×Dic251 | C2 | semidirect |
| 7. C2×#104×C251 | C2 | semidirect |
| 10. #22548713 | C4 | semidirect |
| 11. #22548711 | C4 | semidirect |
| 12. #22548704 | C4 | semidirect |
| 13. #22548702 | C4 | semidirect |
| 49. C4×Dic251 | D4 | semidirect |
| 64. C42×C251 | D4 | semidirect |
| 119. Dic251 | #104 | semidirect |
| 126. C251 | #1962 | semidirect |
| 133. C2×#104 | D251 | semidirect |
| 191. C42 | C22⋊D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632233 | 2 |
| #30631710 | 2 |
| C2×#22548643 | 2 |
| C2×#22548642 | 2 |
| C2×#22548641 | 2 |
| C42×Dic251 | 2 |
| C2×#104×C251 | 2 |
| #1962 | 251 |