Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
332 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 332 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 |
|---|---|---|
| 1. #11927101 | C2 | semidirect |
| 3. #11926946 | C2 | semidirect |
| 4. #11926899 | C2 | semidirect |
| 5. #11926886 | C2 | semidirect |
| 7. #11926840 | C2 | semidirect |
| 8. #11926835 | C2 | semidirect |
| 9. #11926830 | C2 | semidirect |
| 10. #11926825 | C2 | semidirect |
| 11. C19×#431 | C2 | semidirect |
| 135. #431 | D19 | semidirect |
| 172. C19 | #3233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927101 | 2 |
| #11927078 | 2 |
| #11926946 | 2 |
| #11926899 | 2 |
| #11926886 | 2 |
| #11926869 | 2 |
| #11926840 | 2 |
| #11926835 | 2 |
| #11926830 | 2 |
| #11926825 | 2 |
| C19×#431 | 2 |
| #3233 | 19 |