There are lots of amplifier chips. But, what voltage are you supplying to the LM386?

Power is calculated as Voltage x Current, or it can be calculated as V^{2}/R. So for example, with a 5V supply you can get 5V peak-to-peak which is about 1.75V RMS. That's the theoretical maximum and there will be some voltage loss through the amplifier.

So if my calculations are correct, that's about ~~1/4W~~ 0.8W into 4 Ohms or ~~1/8W~~ 0.4W into 8 Ohms. (But since won't get the full voltage, you'll get less than that.)

A bridge amplifier will put-out double the voltage (10V peak-to-peak from a 5V supply) and that can give you 4 times the wattage.