36:6 analog multiplexor?
If you want to spread out the multiplexed outputs among the six inputs, what comes to mind is six 8:1 analog multiplexers, one for each Arduino input.  Two inputs are unused on each chip.

To select the best part, you need to know the output impedances of the sources, the input impedances on the Arduino inputs, and the maximum frequency of interest in the signals being monitored.  All analog switches have an internal resistance or impedance when a channel is "on", and that impedance is not constant; it changes based on the signal voltage.  Look at the CD4051 datasheet for a plot of this.  Ideally you want that resistance to be very small compared to the sum of the source and destination impedances in the complete circuit.

Now that you've added information about the battery, the last questions are the input impedance of the Arduino input and the desired accuracy.