Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
390 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 101 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. C22×#16860794 | C2 | semidirect |
| 2. C2×#22548632 | C2 | semidirect |
| 3. #30631651 | C2 | semidirect |
| 4. #30631456 | C2 | semidirect |
| 27. #16860794 | D4 | semidirect |
| 97. C22×C251 | #100 | semidirect |
| 113. C251 | #1900 | semidirect |
| 211. C22 | #22548632 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860794 | 2 |
| C2×#22548632 | 2 |
| #30631651 | 2 |
| #30631456 | 2 |
| C2×#121×C251 | 2 |
| #1900 | 251 |