Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 2. #30631979 | C2 | semidirect |
| 3. #30631974 | C2 | semidirect |
| 4. #30631969 | C2 | semidirect |
| 5. #30631964 | C2 | semidirect |
| 6. #30631727 | C2 | semidirect |
| 7. #30631711 | C2 | semidirect |
| 9. C2×C4⋊Q8×C251 | C2 | semidirect |
| 36. #16860810 | Q8 | semidirect |
| 72. Dic502 | C2×Q8 | semidirect |
| 74. D1004 | C2×Q8 | semidirect |
| 121. C251 | #3079 | semidirect |
| 123. C2×C4⋊Q8 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#16860810 | 2 |
| #30631979 | 2 |
| #30631974 | 2 |
| #30631969 | 2 |
| #30631964 | 2 |
| #30631727 | 2 |
| #30631711 | 2 |
| #30631686 | 2 |
| C2×C4⋊Q8×C251 | 2 |
| #3079 | 251 |