Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
348 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 121 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. #11926851 | C2 | semidirect |
| 3. #11926836 | C2 | semidirect |
| 4. #11926831 | C2 | semidirect |
| 5. #11926800 | C2 | semidirect |
| 7. #11926766 | C2 | semidirect |
| 8. #11926751 | C2 | semidirect |
| 9. #11926746 | C2 | semidirect |
| 10. #11926568 | C2 | semidirect |
| 11. C19×#533 | C2 | semidirect |
| 129. #533 | D19 | semidirect |
| 176. C19 | #3252 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927078 | 2 |
| #11926851 | 2 |
| #11926836 | 2 |
| #11926831 | 2 |
| #11926800 | 2 |
| #11926792 | 2 |
| #11926766 | 2 |
| #11926751 | 2 |
| #11926746 | 2 |
| #11926568 | 2 |
| C19×#533 | 2 |
| #3252 | 19 |