Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
410 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 137 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. #30632029 | C2 | semidirect |
| 4. #30632023 | C2 | semidirect |
| 5. #30632018 | C2 | semidirect |
| 6. #30631729 | C2 | semidirect |
| 7. #30631697 | C2 | semidirect |
| 25. #22548649 | C22 | semidirect |
| 26. #22548647 | C22 | semidirect |
| 27. #22548640 | C22 | semidirect |
| 28. #22548640 | C22 | semidirect |
| 116. C251 | #3095 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548694 | 2 |
| C2×#22548674 | 2 |
| #30632029 | 2 |
| #30632023 | 2 |
| #30632018 | 2 |
| #30631729 | 2 |
| #30631697 | 2 |
| #407×C251 | 2 |
| #3095 | 251 |