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Made in 1949
Made in 1968
You have a Lewis or NIG model, built in 1903.
It sounds to me that you have a Ithaca Flues model double barrel shotgun.With the serial number that you provided,your shotgun was made by Ithaca in 1917.
If this is an old side by side it would be a Baker model made in 1886. Serial numbers of Ithaca shotguns for that year were 2448 - 4101.
According with Ithaca's web page range 371453501 to 371536500 is from 1975.
shotgun
The gauge is stamped on the water table by the serial number. It is a Flues model made in 1924.
If the shotgun is a hammerless double, it is a Baker Model produced in 1899 (per Dixie Gun Works, Ithaca Serialization Guide) That serial should be a 1926 production NID. sales@countrygunsmith.net
You have an Ithaca NID model made in 1926, Not knowing condition or grade 300 -3500.
I would say that you have a Ithaca model flues double barrel shotgun that was made in the year 1923,with the serial number that you provided.
It your shotgun a Model 37-S or 37-T ?