Amazon Web Service - Designing Mgmt Network

Hi I have a quick question,

i tried to build 1 ubuntu web server instance in AWS with config like below: 1 Ubuntu instance with 2 network interfaces which 1 interface for public (http and https) (eth0) and the other one is for mgmt console (ssh:22) (eth1) and each of the interface have elastic IP.

for security groups config: eth0 have inbound for port 80 and 443 from any ip while eth1 have inbound for port 22 from any ip

below is my interface - VPC config. - public interface (eth0) and mgmt interface (eth1) is at the same VPC but different subnet.

eth0 is at public subnet with public route table (local and internet gateway) eth1 is at private subnet with public route table (local and internet gateway) *later i will change with pvt subnet and allow access only through vpn.

so now the question: above is not working... any idea why? or if you can see what i trying to achieve, then do you have a better idea or design?

thank you in advance! AnD