Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 157 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×#22548740 | C2 | semidirect |
| 2. C2×#22548712 | C2 | semidirect |
| 3. #30632077 | C2 | semidirect |
| 4. #30632063 | C2 | semidirect |
| 5. #30632061 | C2 | semidirect |
| 6. C4×#16860794 | C2 | semidirect |
| 7. #532×C251 | C2 | semidirect |
| 11. C2×#16860797 | C22 | semidirect |
| 12. C2×#16860795 | C22 | semidirect |
| 17. #22548626 | C22 | semidirect |
| 18. C4×C251⋊C8 | C22 | semidirect |
| 20. C4⋊Q8×C251 | C22 | semidirect |
| 21. #127×C251 | C22 | semidirect |
| 22. #124×C251 | C22 | semidirect |
| 35. #16860794 | D4 | semidirect |
| 57. C251⋊C8 | C2×D4 | semidirect |
| 83. C4×C251 | AGL(1,ℤ/8) | semidirect |
| 90. C251 | #3151 | semidirect |
| 93. #532 | D251 | semidirect |
| 106. C4⋊Q8 | C2×D251 | semidirect |
| 110. #127 | C2×D251 | semidirect |
| 111. #124 | C2×D251 | semidirect |
| 174. C4 | #22548740 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548740 | 2 |
| C2×#22548712 | 2 |
| #30632077 | 2 |
| #30632063 | 2 |
| #30632061 | 2 |
| C4×#16860794 | 2 |
| #532×C251 | 2 |
| #3151 | 251 |