Hi,
But you always use 'by' if the means of transport is not modified in any way. 'by train' but 'on/in the last train'. 'by car' but ' on/in Peter's car'... and we say 'on foot (or walking) and 'on horseback', 'on camelback'...rather than 'by horse' or 'by camel'... (not a teacher)
Regards