Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
460 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 127 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×Q16×D251 | C2 | semidirect |
| 4. #30631946 | C2 | semidirect |
| 5. #30631945 | C2 | semidirect |
| 6. #30631942 | C2 | semidirect |
| 7. #30631927 | C2 | semidirect |
| 8. #30631926 | C2 | semidirect |
| 9. #30631722 | C2 | semidirect |
| 10. #30631694 | C2 | semidirect |
| 11. #470×C251 | C2 | semidirect |
| 133. C251 | #3059 | semidirect |
| 141. #470 | 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 |
| C2×#22548723 | 2 |
| #30632260 | 2 |
| #30631946 | 2 |
| #30631945 | 2 |
| #30631942 | 2 |
| #30631927 | 2 |
| #30631926 | 2 |
| #30631722 | 2 |
| #30631694 | 2 |
| #470×C251 | 2 |
| #3059 | 251 |