Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
284 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 97 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. #30631740 | C2 | semidirect |
| 2. C4×C4⋊Dic251 | C2 | semidirect |
| 3. #30631421 | C2 | semidirect |
| 12. C4⋊Q8×C251 | C4 | semidirect |
| 13. #127×C251 | C4 | semidirect |
| 18. C4×D4×C251 | C4 | semidirect |
| 89. C251 | #1502 | semidirect |
| 96. C4⋊Q8 | Dic251 | semidirect |
| 97. #127 | Dic251 | semidirect |
| 102. C4×D4 | Dic251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30631740 | 2 |
| C4×C4⋊Dic251 | 2 |
| #30631421 | 2 |
| #532×C251 | 2 |
| #1502 | 251 |