Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
656 conjugacy classes of subgroups; only the 341 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 341 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. #30631639 | C2 | direct (N × H) |
| 4. C2×#22548626 | C2 | semidirect |
| 5. C2×C8×Dic251 | C2 | semidirect |
| 6. C2×#97×C251 | C2 | semidirect |
| 9. C2×#16860793 | C4 | semidirect |
| 16. #22548626 | C22 | semidirect |
| 17. C8×Dic251 | C22 | semidirect |
| 20. #97×C251 | C22 | semidirect |
| 29. #16860793 | C2×C4 | semidirect |
| 30. C2×C251⋊C8 | C2×C4 | semidirect |
| 37. C2×C8×C251 | C2×C4 | semidirect |
| 45. C2×Dic251 | M16 | semidirect |
| 51. C251⋊C8 | C22×C4 | semidirect |
| 58. C8×C251 | C22×C4 | semidirect |
| 69. Dic251 | C2×M16 | semidirect |
| 70. C2×C251 | C4×M16 | semidirect |
| 74. C251 | C2×C4×M16 | semidirect |
| 80. C2×#97 | D251 | semidirect |
| 94. #97 | C2×D251 | semidirect |
| 109. C2×C8 | C4×D251 | semidirect |
| 133. C8 | C2×C4×D251 | semidirect |
| 146. C2 | #30631639 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860793 | 2 |
| C2×C42×D251 | 2 |
| #30631639 | 2 |
| C2×#22548626 | 2 |
| C2×C8×Dic251 | 2 |
| C2×#97×C251 | 2 |
| C2×C4×M16 | 251 |