Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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. #30632049 | C2 | semidirect |
| 3. #30632044 | C2 | semidirect |
| 4. #30631695 | C2 | semidirect |
| 6. C4×#16860794 | C2 | semidirect |
| 7. #533×C251 | C2 | semidirect |
| 15. #22548638 | C22 | semidirect |
| 17. #22548626 | C22 | semidirect |
| 18. C4×C251⋊C8 | C22 | semidirect |
| 19. C4⋊Q8×C251 | C22 | semidirect |
| 20. #125×C251 | C22 | semidirect |
| 83. C251 | #3140 | semidirect |
| 85. #533 | D251 | semidirect |
| 95. C4⋊Q8 | C2×D251 | semidirect |
| 96. #125 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548703 | 2 |
| #30632049 | 2 |
| #30632044 | 2 |
| #30631695 | 2 |
| #30631691 | 2 |
| C4×#16860794 | 2 |
| #533×C251 | 2 |
| #3140 | 251 |