Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
484 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 255 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 |
|---|---|---|
| 3. #30631715 | C2 | semidirect |
| 4. #30631713 | C2 | semidirect |
| 5. #30631710 | C2 | semidirect |
| 6. C2×Dic251⋊C8 | C2 | semidirect |
| 75. Dic251 | #131 | semidirect |
| 80. C251 | #2906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548722 | 2 |
| #41×Dic251 | 2 |
| #30631715 | 2 |
| #30631713 | 2 |
| #30631710 | 2 |
| C2×Dic251⋊C8 | 2 |
| C2×#131×C251 | 2 |
| #2906 | 251 |