Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
386 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 3. #30632029 | C2 | semidirect |
| 4. #30632029 | C2 | semidirect |
| 5. #30632023 | C2 | semidirect |
| 6. #30632018 | C2 | semidirect |
| 7. #30631729 | C2 | semidirect |
| 8. #30631725 | C2 | semidirect |
| 9. #30631697 | C2 | semidirect |
| 10. C2×#22548640 | C2 | semidirect |
| 126. C251 | #3097 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632258 | 2 |
| #30632170 | 2 |
| #30632029 | 2 |
| #30632023 | 2 |
| #30632018 | 2 |
| #30631729 | 2 |
| #30631725 | 2 |
| #30631697 | 2 |
| C2×#22548640 | 2 |
| #408×C251 | 2 |
| #3097 | 251 |