using the command and factory design patterns for executing queued jobs

I have a list of jobs queued in the database which I need to read from database and execute them in parallel using threading and I have a list of command classes to execute each of those jobs all implementing a common interface (command pattern). but when I retrieve the pending jobs from the database, I will need to instantiate the right command object for each job something like this (in a factory class)

ICommand command;
switch (jobCode)
{
  case "A":
     command = new CommandA();
     break;
  case "B":
     command = new CommandB();
     break;
  case "C":
     command = new CommandC();
     break;
}

command.Execute();

Is there a better way to create the right command object without using a big switch statement like above? OR is there any other pattern for executing the queued jobs?

Solution: solved like this (based on the selected answer). This will do lazy instantiation of the command objects.

public class CommandFactory
{
    private readonly IDictionary<string, Func<ICommand>> _commands;

    public CommandFactory()
    {
        _commands = new Dictionary<string, Func<ICommand>>
                        {
                            {"A", () => new CommandA()},
                            {"B", () => new CommandB()},
                            {"C", () => new CommandC()}
                        };
    }

    public ICommand GetCommand(string jobKey)
    {
        Func<ICommand> command;
        _commands.TryGetValue(jobKey.ToUpper(), out command);
        return command();
    }
}    

Client: 

        var factory = new CommandFactory();
        var command = factory.GetCommand(jobKey);
        command.Execute();