Extracting NDVI for Landcover Classes in Google Earth Engine

I am working on a project where I have created a supervised classification of an image which contains four land cover classes. I have reduced the classification to a frequency histogram that displays the percent land cover taken up by the image, however, I now want to get the NDVI mean for each land cover class.

Using a reducer seems to be the most likely approach but I am not sure how to reduce and match NDVI values associated with each class in this case. The frequency histogram reduction yields the resulting pixel counts:

...
classification: Object (4 properties)
0: 15330.674509803957
1: 7207.431372549016
2: 71314.45098039194
3: 3969.709803921568

Ideally, I would get an object that looks like this:

classification: Object (4 properties)
0: {pixel_count: 15330.674509803957, NDVI: ...}
1: {pixel_count: 7207.431372549016, NDVI: ...}
2: {pixel_count: 71314.45098039194, NDVI: ...}
3: {pixel_count: 3969.709803921568, NDVI: ...}

Does anyone know what the best way to go about computing this reduction would be?

Thanks for any help!