Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
380 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 5. #30631970 | C2 | semidirect |
| 6. #30631895 | C2 | semidirect |
| 8. #30631794 | C2 | semidirect |
| 9. #30631791 | C2 | semidirect |
| 127. C251 | #3113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632239 | 2 |
| C2×Q8×Dic251 | 2 |
| #30632018 | 2 |
| #30632015 | 2 |
| #30631970 | 2 |
| #30631895 | 2 |
| #30631843 | 2 |
| #30631794 | 2 |
| #30631791 | 2 |
| #30631741 | 2 |
| #451×C251 | 2 |
| #3113 | 251 |