Hi in a direct conversion receiver an SRA-6 diode mixer is used. An lm386 after it does not output the volume I like, I need more. I winder if a MC1306 could do the job, does it provide more gain than the lm386, I am confused. Here is the datasheet.
The MC1306 is so old that the datasheet is not available anymore. The datasheet shown here shows that its preamp and its poweramp both have their gains (and high frequency response) determined by their negative feedback.
With the crazy amount of gain your radio needs then oscillation is guaranteed unless you try many different wiring methods.
You mentioned your LM386 with feedback at pin 7 (it is supposed to have a filter capacitor to ground) I have never seen. The datasheet shows a gain of 20 and 200 times and one article shows a resistor in series with a capacitor from pin 1 to ground producing a gain of up to 1800 times! When the gain is increased then the high frequency response is reduced so it might sound very muffled.