Martin's strata: genre, register, discourse semantics, lexicogrammar, phonology
Martin's cline of instantiation: system, genre/register, text type, text, reading.
On this model,
(1) register is simultaneously more abstract than discourse semantics (in terms of stratification) and a sub-system of discourse semantics (in terms of the latter stratum's instantiation);
(2) genre is simultaneously more abstract than register (in terms of stratification), and a sub-system of register (in terms of the latter stratum's instantiation);
(3) register is simultaneously a stratal system and a sub-system of itself (in terms of that stratum's instantiation);
(4) genre is simultaneously a stratal system and a sub-system of itself (in terms of that stratum's instantiation);
etc …
cf Halliday's original (logically coherent) model: