Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
456 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×C22⋊(C251⋊C8) | C2 | semidirect |
| 3. #30631410 | C2 | direct (N × H) |
| 4. C2×C22⋊C8×C251 | C2 | semidirect |
| 15. C22⋊(C251⋊C8) | C22 | semidirect |
| 19. C22⋊C8×C251 | C22 | semidirect |
| 25. C23×D251 | C8 | semidirect |
| 59. C22×D251 | C2×C8 | semidirect |
| 111. C2×C251 | #323 | semidirect |
| 116. C251 | C2×#323 | semidirect |
| 120. C2×C22⋊C8 | D251 | semidirect |
| 136. C22⋊C8 | C2×D251 | semidirect |
| 229. C2 | #30631410 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×(C2×D251)⋊C4 | 2 |
| C2×C22⋊(C251⋊C8) | 2 |
| #30631410 | 2 |
| C2×C22⋊C8×C251 | 2 |
| C2×#323 | 251 |