Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 1. C2×#22548706 | C2 | semidirect |
| 3. #30631996 | C2 | semidirect |
| 4. #30631992 | C2 | semidirect |
| 5. #30631989 | C2 | semidirect |
| 6. #30631985 | C2 | semidirect |
| 7. #30631729 | C2 | semidirect |
| 8. #30631727 | C2 | semidirect |
| 9. #30631710 | C2 | semidirect |
| 135. C251 | #3080 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548706 | 2 |
| #41×Dic251 | 2 |
| #30631996 | 2 |
| #30631992 | 2 |
| #30631989 | 2 |
| #30631985 | 2 |
| #30631729 | 2 |
| #30631727 | 2 |
| #30631710 | 2 |
| #30631688 | 2 |
| #417×C251 | 2 |
| #3080 | 251 |