JavaScript array.sort with multiple values (strings and numbers)

I'd like to sort an array by subject (string, alphabetical), then level (int, ascending), then name (string, alphabetical). I have found numerous other threads on SO but I haven't found any which sort by multiple variable types. I thought I had it, but it isn't sorting properly.

The sort function:

scipads.sort(function (a, b) {
    if (a.subject != b.subject)
        return a.subject < b.subject;
    if (a.level != b.level)
        return a.level - b.level;
    return a.name < b.name;
});

The array:

var scipads = [{
        "name": "L2 Physics Externals",
        "level": 2,
        "subject": "physics",
    }, {
        "name": "L2 Physics Internals",
        "level": 2,
        "subject": "physics",
    }, {
        "name": "L2 Chem Externals",
        "level": 2,
        "subject": "chemistry",
    }, {
        "name": "L2 Chem Internals",
        "level": 2,
        "subject": "chemistry",
    }, {
        "name": "L2 Bio Internals",
        "level": 2,
        "subject": "biology",
    }, {
        "name": "L2 Bio Externals",
        "level": 2,
        "subject": "biology",
    }, {
        "name": "L1 Electricity & Magnetism",
        "level": 1,
        "subject": "physics",
    }, {
        "name": "L1 Wave Behaviour",
        "level": 1,
        "subject": "physics",
    }, {
        "name": "L1 Heat",
        "level": 1,
        "subject": "physics",
    }, {
        "name": "L1 Carbon Chemistry",
        "level": 1,
        "subject": "chemistry",
    }, {
        "name": "L1 Selected Elements",
        "level": 1,
        "subject": "chemistry",
    }, {
        "name": "L1 Chemical Reactions",
        "level": 1,
        "subject": "chemistry",
    },
];

How can I sort by subject, then level, then name?