Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
292 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 292 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. #30631645 | C2 | semidirect |
| 4. C2×#22548626 | C2 | semidirect |
| 5. #30631451 | C2 | semidirect |
| 6. #30631447 | C2 | semidirect |
| 9. #22548722 | C4 | semidirect |
| 16. #22548639 | C4 | semidirect |
| 17. #22548636 | C4 | semidirect |
| 24. #104×C251 | C4 | semidirect |
| 98. C251 | #1765 | semidirect |
| 118. #104 | Dic251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548722 | 2 |
| #30631683 | 2 |
| #30631645 | 2 |
| C2×#22548626 | 2 |
| #30631451 | 2 |
| #30631447 | 2 |
| C2×#104×C251 | 2 |
| #1765 | 251 |