Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
820 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 820 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 |
|---|---|---|
| 2. C2×#22548631 | C2 | semidirect |
| 3. #30631651 | C2 | semidirect |
| 4. #407×C251 | C2 | semidirect |
| 11. C2×#16860794 | C22 | semidirect |
| 15. C2×M16×C251 | C22 | semidirect |
| 67. C22×C251 | #100 | semidirect |
| 83. C251 | #1783 | semidirect |
| 88. #407 | D251 | semidirect |
| 97. C2×M16 | C2×D251 | semidirect |
| 156. C22 | #22548631 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D1004 | 2 |
| C2×#22548631 | 2 |
| #30631651 | 2 |
| #407×C251 | 2 |
| #1783 | 251 |