Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
404 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 123 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×#10597334 | C2 | semidirect |
| 3. #11926948 | C2 | semidirect |
| 4. #11926889 | C2 | semidirect |
| 5. #11926858 | C2 | semidirect |
| 6. #11926857 | C2 | semidirect |
| 7. #11926855 | C2 | semidirect |
| 8. #11926823 | C2 | semidirect |
| 9. #11926822 | C2 | semidirect |
| 10. #11926594 | C2 | semidirect |
| 11. C19×#480 | C2 | semidirect |
| 139. #480 | D19 | semidirect |
| 180. C19 | #3226 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927089 | 2 |
| C2×#10597334 | 2 |
| #11926948 | 2 |
| #11926889 | 2 |
| #11926858 | 2 |
| #11926857 | 2 |
| #11926855 | 2 |
| #11926823 | 2 |
| #11926822 | 2 |
| #11926594 | 2 |
| C19×#480 | 2 |
| #3226 | 19 |