Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
716 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 249 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. #30632165 | C2 | semidirect |
| 3. #30631660 | C2 | semidirect |
| 4. #519×C251 | C2 | semidirect |
| 7. C2×#16860811 | C4 | semidirect |
| 9. C2×Q8×D251 | C4 | semidirect |
| 63. C251 | #2884 | semidirect |
| 67. #519 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548763 | 2 |
| #30632165 | 2 |
| #30631660 | 2 |
| #519×C251 | 2 |
| #2884 | 251 |