Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
484 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 484 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 |
|---|---|---|
| 1. C2×#22548737 | C2 | semidirect |
| 2. #30632265 | C2 | semidirect |
| 3. #30631933 | C2 | semidirect |
| 4. #30631928 | C2 | semidirect |
| 5. #30631923 | C2 | semidirect |
| 6. C2×#22548649 | C2 | semidirect |
| 7. #30631689 | C2 | semidirect |
| 8. C2×#131×C251 | C2 | semidirect |
| 56. C2×C8×C251 | D4 | semidirect |
| 108. C251 | #3061 | semidirect |
| 111. C2×#131 | D251 | semidirect |
| 160. C2×C8 | C22⋊D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548737 | 2 |
| #30632265 | 2 |
| #30631933 | 2 |
| #30631928 | 2 |
| #30631923 | 2 |
| C2×#22548649 | 2 |
| #30631689 | 2 |
| C2×#131×C251 | 2 |
| #3061 | 251 |