She's cold and passive.
Most of the girls in MGE are switches.
There are... 5 full doms and about 10 full subs by my count, but overall most girls are switches.
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It's fun reading through the encyclopedia and I compiled them for you.
These girls will not initiate sex, and even after getting together, their primary way of having sex is by either mind-control charm magicking you, or raising your lust to such unbearable levels
you assault
them.
The rest of the girls are switches. They may dom you, and you can reverse them and turn them into subs, like Orc.
Almost every girl that's not a full sub has a reversal condition except for these girls.
Ogre and ogre sub-species aren't included because ogre's are primal.
Their main race text says they'll submit to someone who can sexually outperform them, and the sub-species don't contradict that.
Remember, that's just based on what the encylopedia guy says, and he's an in-world character with his own biases. The girls aren't exactly like what he says so there's probably some variation. For the sake of discussion and everyone's shared understanding, I follow it.
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Back to Phoenix.
Phoenix shows no sexual assertiveness.
In fact the man has to initiate and pursue relationships with her so she's passive. But that doesn't necessarily mean she's submissive sexually. Passive girls usually are submissive, but not so much in MGE.
A switch that leans sub is what I'd consider her.