According to SOWPODS (the combination of Scrabble dictionaries used around the world) there are 28 words with the pattern -EG-I–. That is, seven letter words with 2nd letter E and 3rd letter G and 5th letter I. In alphabetical order, they are:
begging
begoing
begrime
begrims
beguile
beguine
beguins
degging
geggies
kegging
kegling
leggier
legging
leggins
leggism
leglike
leglins
megrims
neglige
peggies
peghing
peglike
regains
regrind
tegmina
veggies
vegging
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