Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
500 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 1. C2×#22548746 | C2 | semidirect |
| 3. C2×#22548704 | C2 | semidirect |
| 4. #30632155 | C2 | semidirect |
| 5. #30631912 | C2 | semidirect |
| 6. #30631905 | C2 | semidirect |
| 7. #30631710 | C2 | semidirect |
| 8. #30631691 | C2 | semidirect |
| 9. #419×C251 | C2 | semidirect |
| 14. C2×#16860800 | C22 | semidirect |
| 16. C2×#16860797 | C22 | semidirect |
| 22. #22548680 | C22 | semidirect |
| 23. #22548677 | C22 | semidirect |
| 29. Dic251⋊C8 | C22 | semidirect |
| 34. #103×C251 | C22 | semidirect |
| 125. C251 | #3040 | semidirect |
| 134. #419 | D251 | semidirect |
| 159. #103 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548746 | 2 |
| C2×#22548743 | 2 |
| C2×#22548704 | 2 |
| #30632155 | 2 |
| #30631912 | 2 |
| #30631905 | 2 |
| #30631710 | 2 |
| #30631691 | 2 |
| #419×C251 | 2 |
| #3040 | 251 |