I am trying to produce a bar graph that has multiple groupings of factors. An example from excel of what I am attempting to create, subgrouped by Variety and Irrigation treatment:

I know I could produce multiple graphs using facet_wrap(), but I would like to produce multiple graphs for this same type of data for multiple years of similar data. An example of the data I used in this example:
Year        Trt Variety    geno yield   SE
2010-2011   Irr Variety.2   1   6807    647
2010-2011   Irr Variety.2   2   5901    761
2010-2011   Irr Variety.1   1   6330    731
2010-2011   Irr Variety.1   2   5090    421
2010-2011   Dry Variety.2   1   3953    643
2010-2011   Dry Variety.2   2   3438    683
2010-2011   Dry Variety.1   1   3815    605
2010-2011   Dry Variety.1   2   3326    584
Is there a way to create multiple groupings in ggplot2? I have searched for quite some time and have yet to see an example of something like the example graph above.
Thanks for any help you may have!
 