Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
552 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 552 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×#22548747 | C2 | semidirect |
| 2. C2×#22548744 | C2 | semidirect |
| 4. C4⋊Q8×D251 | C2 | semidirect |
| 5. #30632082 | C2 | semidirect |
| 6. #30632081 | C2 | semidirect |
| 7. #30632079 | C2 | semidirect |
| 8. #30632065 | C2 | semidirect |
| 9. #30632058 | C2 | semidirect |
| 10. #30631639 | C2 | semidirect |
| 11. #497×C251 | C2 | semidirect |
| 63. #16860793 | D4 | semidirect |
| 124. Dic251 | #137 | semidirect |
| 130. C251 | #3152 | semidirect |
| 139. #497 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548747 | 2 |
| C2×#22548744 | 2 |
| #30632236 | 2 |
| C4⋊Q8×D251 | 2 |
| #30632082 | 2 |
| #30632081 | 2 |
| #30632079 | 2 |
| #30632065 | 2 |
| #30632058 | 2 |
| #30631639 | 2 |
| #497×C251 | 2 |
| #3152 | 251 |