This grouping is what frequency modulation looks like whenever the input to the modulator is a constant single tone of a fairly high frequency.
(If the tone were of a much lower frequency, then you would instead see a single peak moving in a sinusoidal fashion as a straightforward understanding of frequency modulation would suggest. This can be observed on repeater transmissions that use CTCSS tones, with a fast waterfall.)
The single tone that is present but that you are not hearing is the 19 kHz (higher than audible, and usually filtered out by a receiver) “pilot” tone for FM stereo encoding.
FM broadcast stereo works by taking the two stereo audio channels and rearranging them into a single channel where everything but the combined mono signal is of a higher-than-audible frequency. Wikipedia has a nice chart (including some additional features beyond stereo):
This is not a plot of RF frequencies. This is the signal which is sent into the FM modulator in place of the audio signal which a mono transmitter would use — note that the 0 to 15 kHz audible range is just audio. (This is for compatibility with mono receivers.)
When the stereo audio is silent, the L+R and L−R outputs are both silent, so the only thing in the signal (assuming none of the additional digital features charted above are present) is the 19 kHz tone.
The purpose of that “pilot tone” is to allow the FM stereo decoder in the receiver to precisely locate the frequency-shifted stereo difference audio (at twice the pilot tone frequency; can be seen as DSB-SC modulation) and shift it back, despite any drift in the relevant oscillators.
Again, the pilot tone is at a single frequency; it is just the case that when that single tone goes through a FM modulator, a theoretically infinite (and in practice bandlimited) collection of sidebands is produced, which is the way FM always works.