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6 letter words:

loggia8,

5 letter words:

logia6,

4 letter words:

agog6, giga6, agio5, gaol5, glia5, goal5,

3 letter words:

gag5, gig5, igg5, ago4, gal4, goa4, lag4, log4, ail3, oil3,

2 letter words:

ag3, go3, ai2, al2, la2, li2, lo2, oi2,