Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
312 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 79 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. #30631696 | C2 | semidirect |
| 5. #30631444 | C2 | semidirect |
| 6. #30631443 | C2 | semidirect |
| 7. #419×C251 | C2 | semidirect |
| 13. #22548713 | C4 | semidirect |
| 14. #22548704 | C4 | semidirect |
| 109. C251 | #1909 | semidirect |
| 114. #419 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632453 | 2 |
| #30632261 | 2 |
| #30631696 | 2 |
| #30631660 | 2 |
| #30631444 | 2 |
| #30631443 | 2 |
| #419×C251 | 2 |
| #1909 | 251 |