You can use a script in the python window to achieve this. I did a quick test with a 96 feature dataset which I split into shapefiles of 8 features each.
If you enter the following into the python window (minus the notes after the #), making changes for variables such as the number of features per featureclass, layer name, output path etc., you should have success.
outputBaseFile = r"C:\OUTPUTPATH\NEWFILENAME_"
reqNum = 8 #features per featureclass
totalFeatures = float((arcpy.GetCount_management("YOUR_LAYER")).getOutput(0)) #this counts the number of features in your data
maxReps = ceil(totalFeatures / reqNum) #this determines the number of new feature classes
count = 1
startNum = 1
while count <= maxReps:
sqlQuery = '"OBJECTID" >= ' + str(startNum) + ' AND "OBJECTID" <= ' + str(reqNum * count)
outputFile = outputFileBase + str(startNum) + "_to_" + str(reqNum * count) + ".shp"
count += 1
startNum += reqNum
Note that in this code I just named the files with the ranges each would contain, and even though my last file only had seven features, it was still named with an 8 number range. This was just to save time writing, and you could implement your own solution to apply the correct range to the final file. Of course, you could use a totally different method for identifying your output files.