Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
816 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 309 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. #30631562 | C2 | semidirect |
| 3. #30631547 | C2 | semidirect |
| 6. C2×C4⋊Dic251 | C22 | semidirect |
| 10. C251⋊#95 | C22 | semidirect |
| 13. C2×C22⋊C4×C251 | C4 | semidirect |
| 28. C22×C4×C251 | C2×C4 | semidirect |
| 30. C22⋊C4×C251 | C2×C4 | semidirect |
| 39. C23×C251 | C4⋊C4 | semidirect |
| 71. C251 | #2315 | semidirect |
| 84. C2×C22⋊C4 | Dic251 | semidirect |
| 97. C22×C4 | C2×Dic251 | semidirect |
| 102. C22⋊C4 | C2×Dic251 | semidirect |
| 108. C23 | C4⋊Dic251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊Dic251 | 2 |
| #30631562 | 2 |
| #30631547 | 2 |
| C22×C22⋊C4×C251 | 2 |
| #2315 | 251 |