Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
296 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 97 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×#22548651 | C2 | semidirect |
| 2. #30631696 | C2 | semidirect |
| 4. C2×#22548634 | C2 | semidirect |
| 6. #30631642 | C2 | semidirect |
| 24. C2×SD16×C251 | C4 | semidirect |
| 106. C251 | #1977 | semidirect |
| 120. C2×SD16 | Dic251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548651 | 2 |
| #30631696 | 2 |
| #30631692 | 2 |
| C2×#22548634 | 2 |
| C2×#22548632 | 2 |
| #30631642 | 2 |
| C22×SD16×C251 | 2 |
| #1977 | 251 |