The top part of「姜」is「羊」, serving as a phonetic component, and the bottom part is「女」, serving as a semantic component. It was originally used as a proper noun.
This is where the clarity ends if you rely on things like popular etymology or non-up to date resources to check up similar-looking characters, which will frequently provide conflicting or obscure explanations for glyph origins (although most resources will decompose「姜」correctly).
In general, Chinese character components have changed heavily over the years, with different components sometimes merging into one form. Most references that you'll see will not give you a clear breakdown of individual characters, and the times they get an individual component「X」right do not explain other components which have merged into the same shape as「X」.
As others have correctly stated, 「⺷」is how we write「羊」at the top in the modern form. There is one more (actually two, but they're very similar graphical variations of each other) shape morph of「羊」to be aware of, and that is how it's written at the top-left:
- 「⺶」(PRC usually uses this form)
- 「⿱𦍌⿰丿X」, where X is a placeholder (Other places usually use this form)
I won't talk about characters which contain the full form of「羊」here, like「咩」or「羶」, because they're fairly obvious. Characters which really contain the graphical variants of「羊」described above can be split into the following:
Characters which had a hint of the meaning sheep. Examples:
- 「羔」, a lamb
- 「義」, morality
- 「善」, a meal (now written「膳」)
- 「犧」, to sacrifice
- 「羞」, (original meaning) an offering
Characters which had a hint of the sound ancestral to yáng. Examples:
- 「姜」, jiāng
- 「羕」, yàng
- 「恙」, yàng
Characters which uses「羊」for both sound and meaning. Examples:
- 「羌」, qiāng, the historical Qiang tribes which were constantly at war with the Shang dynasty. These people were perceived by the Shang to wear ram horns as a sort of decorative or ritualistic headwear.
- 「養」, yǎng, (original meaning) to herd sheep
There are many other characters which don't really contain「羊」, but was something else that eventually morphed into「𦍌」, 「⺶」, or「⿱𦍌⿰丿X」. Examples:
- 「着」, large graphical corruptions of what was originally「箸」
- 「美」, top was originally a headdress
- 「差」, top was originally「木」
- 「盖」, top was originally「去」
- 《古文字詁林》, 1999
- 季旭昇《說文新證》, 2014