Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
388 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 388 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 |
|---|---|---|
| 1. C2×C22⋊(C251⋊C8) | C2 | semidirect |
| 2. C2×C251⋊#95 | C2 | semidirect |
| 3. #30631421 | C2 | direct (N × H) |
| 8. C22⋊(C251⋊C8) | C22 | semidirect |
| 10. C251⋊#95 | C22 | semidirect |
| 12. C22×D4×C251 | C4 | semidirect |
| 16. #121×C251 | C4 | semidirect |
| 18. C2×C4⋊C4×C251 | C4 | semidirect |
| 34. C2×D4×C251 | C2×C4 | semidirect |
| 44. C4⋊C4×C251 | C2×C4 | semidirect |
| 107. C2×C251 | #327 | semidirect |
| 111. C251 | C2×#327 | semidirect |
| 118. C22×D4 | Dic251 | semidirect |
| 124. #121 | Dic251 | semidirect |
| 126. C2×C4⋊C4 | Dic251 | semidirect |
| 140. C2×D4 | C2×Dic251 | semidirect |
| 156. C4⋊C4 | C2×Dic251 | semidirect |
| 219. C2 | #30631421 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊(C251⋊C8) | 2 |
| C2×C251⋊#95 | 2 |
| #30631421 | 2 |
| C2×#121×C251 | 2 |
| C2×#327 | 251 |