Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
362 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 362 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. #30631997 | C2 | semidirect |
| 4. #30631993 | C2 | semidirect |
| 5. #30631981 | C2 | semidirect |
| 6. #30631971 | C2 | semidirect |
| 44. C2×Dic502 | Q8 | semidirect |
| 116. C251 | #3082 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632315 | 2 |
| #30632164 | 2 |
| #30631997 | 2 |
| #30631993 | 2 |
| #30631981 | 2 |
| #30631971 | 2 |
| #30631730 | 2 |
| #30631713 | 2 |
| #30631695 | 2 |
| C2×#22548640 | 2 |
| #427×C251 | 2 |
| #3082 | 251 |