Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
358 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 3. #30631991 | C2 | semidirect |
| 4. #30631894 | C2 | semidirect |
| 6. #30631792 | C2 | semidirect |
| 7. C4×#16860800 | C2 | semidirect |
| 95. C251 | #3127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632164 | 2 |
| #30632025 | 2 |
| #30631991 | 2 |
| #30631894 | 2 |
| #30631842 | 2 |
| #30631792 | 2 |
| C4×#16860800 | 2 |
| #30631748 | 2 |
| #541×C251 | 2 |
| #3127 | 251 |