Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
424 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 119 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. C2×#22548680 | C2 | semidirect |
| 3. #30632000 | C2 | semidirect |
| 4. #30631981 | C2 | semidirect |
| 5. #30631886 | C2 | semidirect |
| 6. #30631828 | C2 | semidirect |
| 7. #30631825 | C2 | semidirect |
| 8. #30631786 | C2 | semidirect |
| 9. #30631784 | C2 | semidirect |
| 10. #30631741 | C2 | semidirect |
| 11. #480×C251 | C2 | semidirect |
| 86. Dic502 | #41 | semidirect |
| 140. C251 | #3112 | semidirect |
| 145. #480 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632232 | 2 |
| C2×#22548680 | 2 |
| #30632000 | 2 |
| #30631981 | 2 |
| #30631886 | 2 |
| #30631828 | 2 |
| #30631825 | 2 |
| #30631786 | 2 |
| #30631784 | 2 |
| #30631741 | 2 |
| #480×C251 | 2 |
| #3112 | 251 |