As no explicit question is asked, I assume that the question is this: Are Bhakti Yoga and Raja Yoga part of either Gnana Yoga or Karma Yoga? No, they are not:
Bhakti Yoga: The Path of Devotion
God's love is unconditional. Acknowledging that
love and reflecting it back is devotion. The blossoming of devotion
towards God is the sweetest experience one can have.
Devotion means being in a state of complete surrender to God. It is
the desire to serve God, accompanied by love and gratitude. A devotee
sees Divinity everywhere and yet has an intense longing for the
Divine. Bhakti Yoga is one of the types of yoga mentioned in the
ancient Indian scripts which denotes the spiritual practice of
lovingly devoting oneself to a personal form of God. Bhakti is a
Sanskrit term for devotion.
Love towards God can take many forms with many different feelings: A
true friendship with God, being a faithful servant to God, being a
beloved of God, being a child of God, being a parent to God.
devotion, one can experience total freedom from fear and worry. A
devotee transcends worldly sorrows and pains.
A true devotee has no selfish desires, including the desire for
liberation. Devotion in one's heart is kindled by the grace of the
Guru, by being in the company of other devotees and by reading and
listening to the stories of other devotees.
“When the river meets the ocean, it recognizes it is the ocean from
the beginning to the end. In the same way, the moment a devotee
surrenders to the Divine, the devotee becomes Divine.”
The above is from an article by Sri Sri Ravi Shankar: http://www.artofliving.org/in-en/bhakti-yoga
Also, Raja Yoga is different. Also called the Path of the Royals, it is the path of knowledge that was given to highly evolved kings. A lot of secrets are given which are only meant for the ruler and not the common people. Hence, not much is talked about this.