Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
400 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 129 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. #30632240 | C2 | semidirect |
| 3. #30632043 | C2 | semidirect |
| 4. #30632040 | C2 | semidirect |
| 5. #30632036 | C2 | semidirect |
| 6. #30632032 | C2 | semidirect |
| 7. #30631684 | C2 | semidirect |
| 8. #30631683 | C2 | semidirect |
| 9. #30631681 | C2 | semidirect |
| 10. C2×C8×Dic251 | C2 | semidirect |
| 11. #416×C251 | C2 | semidirect |
| 125. C251 | #3131 | semidirect |
| 136. #416 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632240 | 2 |
| #30632233 | 2 |
| #30632043 | 2 |
| #30632040 | 2 |
| #30632036 | 2 |
| #30632032 | 2 |
| #30631684 | 2 |
| #30631683 | 2 |
| #30631681 | 2 |
| C2×C8×Dic251 | 2 |
| #416×C251 | 2 |
| #3131 | 251 |