My table below lists thousands of barrels.
1. Jos. Schlitz / 5940
2. Anheuser-Busch / 5865
3. P. Ballantine / 3966
4. Falstaff / 3870
5. Pabst / 3400
6. Theo. Hamm / 3374
7. Liebmann / 3000
8. Carling / 2996
9. F&M Schaefer / 2720
10. Stroh / 2708
11. Miller / 2245
12. Lucky / 1960
13. C. Schmidt / 1850
14. Drewrys Ltd / 1434
15. Piel Bros. / 1350
16. Adolph Coors / 1090
17. Jackson / 1051
18. Duquesne / 1045
19. Burgermeister / 1033
20 Pfeiffer / 1028
21. Blatz / 949
22. Pearl / 904
23. Narragansett / 850
24. Geo. Wiedemann / 835
25. International / 810
26. Goebel / 807
27. Gunther / 800
28. Pittsburgh / 781
29. Lone Star / 752
30. G. Krueger / 584
31. Regal Pale / 472
32. Minneapolis / 517
33. G. Heileman / 461
34. West End / 451
36. Heidelberg / 406
37. Erie / 314
38. Fort Pitt / 234
39. Kingsbury / 200
40. L. F. Neuweiler's Sons / 192
41. American / 186
42. Standard / 177
43. Metropolis / 161
44. E & B / 150
45. Wm. Gretz / 146
46. Horlacher / 139
47. Great Falls / 126
48. Sunshine / 123
49. Independent Milwaukee / 118
50. Dixie / 118
A couple observations:
1. Note says "Schlitz led over next largest brewery [AB] by 75,000 barrels...Schlitz led over next largest brand by estimated 400,000 barrels." From this we can assume that Anheuser-Busch's combined sales of non-Budweiser brands in 1956 were 325,000 barrels, roughly 6% of their output.
2. It's interesting to see which apparently minor breweries (American, E & B, Sunshine) make the top 50.
3. At the same time, the massive dropoff in production figures (#50, Dixie, produces 2% of what Schlitz produces) gives evidence that the consolidation around megabreweries was already well under way. How many of these 50 breweries were dead 15 years later?
4. As a California collector, I'm surprised to see how comparatively small the big California breweries are in 1956. Just anecdotally, you'd think that cans from #12 Lucky and #13 C. Schmidt would be similarly common, but no. Harder (even here in the east) to come up with #18 Duquesne cans than #19 Burgermeister cans. And so on. Dumping success distorts my assumptions about how big a brewery must have been.