Unexpected results when casting dword to byte [4] (endianity swap?)

Unexpected results when casting dword to byte [4] (endianity swap?)

Im trying to cast a dword into an array of 4 bytes. When i do this, the
bytes seem to flip around (change endianness)
As i understand it a dword equaling 0x11223344 on little endian systems
will look like this:
0000_1011___0001_0110___0010_0001____0010_1100
but when i do this:

typedef unsigned long dword;
typedef unsigned char byte;
int main(void)
{
dword a = 0x11223344;
byte b[4];
memcpy(b, &a, 4);
printf("%x %x %x %x\n", b[0], b[1], b[2], b[3]);
}
I get 44 33 22 11.
I expected it to be 11 22 33 44.

The same thing happens when i use reinterpret_cast or
union
{
dword a;
byte b[4];
} foo;
Im guessing Im wrong and not the compiler/processor, but what am i missing
here? Also how would this look on a big endian system?