Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
344 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 125 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×C4⋊(C251⋊C8) | C2 | semidirect |
| 3. #30631416 | C2 | direct (N × H) |
| 4. C2×C4×C8×C251 | C2 | semidirect |
| 15. C4⋊(C251⋊C8) | C22 | semidirect |
| 19. C4×C8×C251 | C22 | semidirect |
| 23. C2×D1004 | C8 | semidirect |
| 51. D1004 | C2×C8 | semidirect |
| 88. C2×C251 | D4⋊C8 | semidirect |
| 93. C251 | C2×D4⋊C8 | semidirect |
| 97. C2×C4×C8 | D251 | semidirect |
| 113. C4×C8 | C2×D251 | semidirect |
| 183. C2 | #30631416 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D1004 | 2 |
| C2×C4⋊(C251⋊C8) | 2 |
| #30631416 | 2 |
| C2×C4×C8×C251 | 2 |
| C2×D4⋊C8 | 251 |