Find the missing number in the series:
$$1,12,144,\dots ,20736$$

Let's look at the operational pattern of the terms in the given sequence:
* $1^{\text{st}}\text{ term}=1$
* $2^{\text{nd}}\text{ term}=1\times 12=12$
* $3^{\text{rd}}\text{ term}=12\times 12=144$

The terms follow a geometric progression where each term is multiplied by a common ratio of $12$ to get the next term.

Following this pattern, the missing $4^{\text{th}}$ term must be:

$$4^{\text{th}}\text{ term}=144\times 12=1728$$

Let's check the next term to verify consistency:

$$5^{\text{th}}\text{ term}=1728\times 12=20736$$

This matches the final term perfectly. Hence, the missing number is $1728$.