As previously mentioned, mixed Geometries in one layer are not supported by QGIS.

If you have strong use case for keeping all of the data in a single table, another option to creating new tables (as suggested by @Benno) would be to create views referencing each geometry type from the initial table:

    CREATE VIEW vwPoints 
    SELECT <fields> 
    FROM initial_table 
    WHERE ST_GeometryType(geom) = 'ST_Point'

I am not sure about is the performance implications of going with views vs. individual tables, but that is something you could easily experiment with and decide which route you want to take.