Not so simple. ;-) There are several different lengths of Hotchkiss 3.67"-caliber base cups.
Assuming you want it for putting onto a Hotchkiss nose, you'll need to figure out exactly which version of 3.67"-caliber Hotchkiss nose you've got, and then get the correct base cup matchup for your nose.
Because the long-bodied 3.67"-caliber Hotchkiss projectiles made for use in a 20-pounder Parrott Rifle are so rare, I'll assume your Hotchkiss nose is the shorter version for a Rifled 6-pounder Smoothbore cannon. Here's a list of the Hotchkiss varieties for that type of cannon.
Rifled 6-pounder, Bolt (none have flamegrooves)
R6p, wood timefuzed, without flamegrooves
R6p, wood timefuzed, with flamegrooves
R6p, solder timefuze, without flamegrooves
R6p, solder timefuze, with flamegrooves
R6p, brass timefuze, Common-shell (all have flamegrooves)
R6p, brass timefuze, Case-Shot (all have flamegrooves)
R6p, iron Percussion fuze (none have flamegrooves)
R6p, brass Percussion fuze (none have flamegrooves)
On the above varieties, some have a very short base cup, or a longer one, and some have a rounded bottom, and some have a nearly-flat bottom. Compare the photos in the Dickey-&-George book.
Regards,
Pete