Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
224 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 224 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 |
|---|---|---|
| 4. #30631409 | C2 | semidirect |
| 5. #30631408 | C2 | semidirect |
| 6. C8×C251⋊C8 | C2 | semidirect |
| 7. C82×C251 | C2 | semidirect |
| 24. #16860793 | C8 | direct (N × H) |
| 45. C251⋊C8 | C2×C8 | semidirect |
| 50. C8×C251 | C2×C8 | semidirect |
| 51. C8×C251 | M16 | semidirect |
| 66. C251 | C8×M16 | semidirect |
| 74. C82 | D251 | semidirect |
| 117. C8 | C8×D251 | semidirect |
| 118. C8 | #16860793 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30631738 | 2 |
| C4×#16860793 | 2 |
| C4×C8×D251 | 2 |
| #30631409 | 2 |
| #30631408 | 2 |
| C8×C251⋊C8 | 2 |
| C82×C251 | 2 |
| C8×M16 | 251 |