Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
456 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 175 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. #30631795 | C2 | semidirect |
| 4. #30631794 | C2 | semidirect |
| 5. #30631793 | C2 | semidirect |
| 6. C4×#16860800 | C2 | semidirect |
| 7. #30631779 | C2 | semidirect |
| 11. #441×C251 | C2 | semidirect |
| 15. Q16×D251 | C4 | semidirect |
| 108. C251 | #2950 | semidirect |
| 115. #441 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D251 | 2 |
| #30632163 | 2 |
| #30631795 | 2 |
| #30631794 | 2 |
| #30631793 | 2 |
| C4×#16860800 | 2 |
| #30631779 | 2 |
| #30631722 | 2 |
| #30631694 | 2 |
| #30631644 | 2 |
| #441×C251 | 2 |
| #2950 | 251 |