Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
480 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 149 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×#22548715 | C2 | semidirect |
| 4. #30631898 | C2 | semidirect |
| 5. #30631893 | C2 | semidirect |
| 6. #30631697 | C2 | semidirect |
| 7. #423×C251 | C2 | semidirect |
| 87. C4×C251 | #137 | semidirect |
| 97. C251 | #3039 | semidirect |
| 104. #423 | D251 | semidirect |
| 188. C4 | #22548748 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548748 | 2 |
| C2×#22548715 | 2 |
| C4×#16860810 | 2 |
| #30631898 | 2 |
| #30631893 | 2 |
| #30631697 | 2 |
| #423×C251 | 2 |
| #3039 | 251 |