Exploring the partitioning of different numbers of clusters can be done by hand, by repeatedly running a code like this:

#load iris data
    x = iris[,-5]
    y = iris$Species
#kmeans for 3 clusters
    N = 3
    kc <- kmeans(x, N)
# plot kmeans output    
ggplot() + 
    geom_point(aes(x$`Sepal.Length`, x$`Sepal.Width`), col=kc$cluster, 
               shape = as.numeric(y), size = 2) +
    geom_point(aes(kc$centers[, "Sepal.Length"], 
                   kc$centers[, 'Sepal.Width']), col=1:N, size = 5) +
    labs(x = "Sepal length", y = "Sepal width", 
         title = paste(N, "clusters")) +
    theme_classic()

And several plots are produced to be compared.

Please, visit https://bhenning.shinyapps.io/bhApp/

On the top right pannel the user can see the clustering classification plots.

On the bottom right pannel the user can see centroid values for each cluster.