Highly symmetric networks can exhibit partly symmetry-broken states, including clusters and chimera states, i.e., states of coexisting synchronized and unsynchronized elements. We address the ${\mathbb{S}}_4$ permutation symmetry of four globally coupled Stuart-Landau oscillators and uncover an interconnected web of solutions with different symmetries. Among these are chaotic $2-1-1$ minimal chimeras that arise from $2-1-1$ periodic solutions in a period-doubling cascade, as well as fully asymmetric chaotic states arising similarly from periodic $1-1-1-1$ solutions. A backbone of equivariant pitchfork bifurcations mediate between the two cascades, culminating in equivariant pitchforks of chaotic attractors.

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• Bifurcations
• Chaos
• Chimera states
• Collective dynamics
• Coupled oscillators
• Dynamics of networks