When Nick states that Daisy "asserted her membership in a rather distinguished secret society to which she and Tom belonged," he infers to the...

The line with which this question is referring to is found in chapter 1 on page 17. Preceding this line, Nick and Daisy talk on the porch following dinner. It is during this talk that Daisy shares with Nick how unhappy she is with her life and marriage with Tom. In this exchange, Daisy reveals how unhappy she is with her daughter and that: "I think everything's terrible anyhow." She follows up by saying...

The line with which this question is referring to is found in chapter 1 on page 17. Preceding this line, Nick and Daisy talk on the porch following dinner. It is during this talk that Daisy shares with Nick how unhappy she is with her life and marriage with Tom. In this exchange, Daisy reveals how unhappy she is with her daughter and that: "I think everything's terrible anyhow." She follows up by saying "Everybody thinks so-the most advanced people." She further goes on to say she knows this because she has been everywhere and done everything:

I’ve been everywhere and seen everything and done everything.” Her eyes flashed around her in a defiant way...

Her attitude is a by-product of the insincere, sarcastic, bitter cynicism she lives with that results from Tom's dalliances with other women (other women is why she "wept" upon hearing she had a daughter).

This leads the reader to infer that the "secret society" Daisy's smirk (an unpleasant smile indicating pleasure at someone else's misfortune or feelings of self-superiority) makes Nick think of relates to Tom's "woman," the bitterness Daisy finds in being "a girl," and the false value of being "sophisticated" in the company of the "most advanced people."

she laughed with thrilling scorn. “Sophisticated — God, I’m sophisticated!”