Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 133 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. #30632028 | C2 | semidirect |
| 3. #30632022 | C2 | semidirect |
| 4. #30632011 | C2 | semidirect |
| 5. #30632000 | C2 | semidirect |
| 6. #30631730 | C2 | semidirect |
| 7. C2×#22548648 | C2 | semidirect |
| 8. #30631686 | C2 | semidirect |
| 9. #30631681 | C2 | semidirect |
| 10. #30631654 | C2 | semidirect |
| 11. #520×C251 | C2 | semidirect |
| 133. C251 | #3098 | semidirect |
| 136. #520 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632265 | 2 |
| #30632028 | 2 |
| #30632022 | 2 |
| #30632011 | 2 |
| #30632000 | 2 |
| #30631730 | 2 |
| C2×#22548648 | 2 |
| #30631686 | 2 |
| #30631681 | 2 |
| #30631654 | 2 |
| #520×C251 | 2 |
| #3098 | 251 |