Such as genders that are not 'man' or 'woman'.
Not a very difficult question.
I mean, if you blindly think gender is directly tied to biology and then further claim that there is only two sexes then why would ask such an asinine question "such as?" instead of simply answering the question?
I know some people like to call "intersex" a 3rd gender, I thought that was where you were going with it. However to answer your question, it's not that I am against it, but rather I don't see them as genders; what you call gender I will probably call something else.
But since I strongly suspect an "anything but Greek" response:
en.wikipedia.org
There are many types of gender identity. Learn more about their definitions, the difference between sex and gender, and how gender exists on a spectrum here.
www.medicalnewstoday.com
How many genders are there? Besides male and female, here is a list of all 72 other gender identities that a person may belong to. How can I help my child understand gender identity?
www.medicinenet.com
Our gender identity is how we feel about our bodies, inside and out, and how we present and relate to this feeling in our environment. No two people will have the exact same gender expression, as it has more to do with how one feels inside and the experience is a personal one.
www.choosingtherapy.com
There are quite a few more lists if that is not enough.
I looked at a few and their descriptions
Androgyne: To possess both Masculine and Feminine characteristics.
Isn't that just about everybody? Doesn't everybody of various degrees have a masculine and feminine side?
Bigender: Not solely male or female.
If not 100% male or female characteristics, how is that different from Androgyne?
Femme: Lesbian who presents as feminine
Butch Lesbian who presents as Masculine
There were lots of them, but as I said before, I just don't see them as a gender, but something else.