Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
384 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 157 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. C2×C8×Dic251 | C2 | semidirect |
| 5. #30631442 | C2 | semidirect |
| 6. #30631441 | C2 | semidirect |
| 7. C2×C4×C8×C251 | C2 | semidirect |
| 13. C2×C8×D251 | C4 | semidirect |
| 16. (C2×D251)⋊C8 | C4 | semidirect |
| 39. (C2×D251)⋊C4 | C8 | direct (N × H) |
| 62. C2×Dic251 | C2×C8 | semidirect |
| 72. C2×C4×C251 | C2×C8 | semidirect |
| 80. C8×C251 | C22⋊C4 | semidirect |
| 90. C2×D251 | C4×C8 | semidirect |
| 104. C251 | C8×C22⋊C4 | semidirect |
| 109. C2×C4×C8 | D251 | semidirect |
| 175. C2×C4 | C8×D251 | semidirect |
| 185. C8 | (C2×D251)⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D251 | 2 |
| C2×(C2×D251)⋊C8 | 2 |
| C2×C8×Dic251 | 2 |
| C4×(C2×D251)⋊C4 | 2 |
| #30631442 | 2 |
| #30631441 | 2 |
| C2×C4×C8×C251 | 2 |
| C8×C22⋊C4 | 251 |