Check the below input data and expected output to sort the IP-Addresses in the correct order.
(Use PARSENAME() for splitting the IP-Addresses into four parts and then get the correct sorted result)
Input Data:

IPAddress
---------------
25.120.144.0
16.16.8.8
116.226.0.1
1.240.255.255
1.0.180.160
122.42.1.10
255.255.16.8
120.140.1.2
1.166.10.44

Expected Output:

IPAddress
---------------
1.0.180.160
1.166.10.44
1.240.255.255
16.16.8.8
25.120.144.0
116.226.0.1
120.140.1.2
122.42.1.10
255.255.16.8

Create a table with data:

CREATE TABLE NetworkData 
( 
	[IPAddress]  VARCHAR(15) 
)
GO

INSERT INTO NetworkData 
VALUES 
('25.120.144.0')
,('16.16.8.8')
,('116.226.0.1')
,('1.240.255.255')
,('1.0.180.160')
,('122.42.1.10')
,('255.255.16.8')
,('120.140.1.2')
,('1.166.10.44')
GO

Solution: Using PARSENAME()

SELECT [IPAddress] 
FROM NetworkData
ORDER BY CAST(PARSENAME([IPAddress], 4) AS INT)
         ,CAST(PARSENAME([IPAddress], 3) AS INT)
         ,CAST(PARSENAME([IPAddress], 2) AS INT)
         ,CAST(PARSENAME([IPAddress], 1) AS INT)

Please try the different solution for this puzzle and share it via comment...

PostgreSQL provides Network Address related data types for storing information like IP Addresses, Mac Addresses.

If you are planning to store the IP Address in PostgreSQL Database, you should declare the INET data type for that column.
Internally, It checks the format of data so you cannot insert invalid format of data.

The input format for this type is address/y where address is an IPv4 or IPv6 address and y is the number of bits in the netmask.
If the /y portion is missing, the netmask is 32 for IPv4 and 128 for IPv6, so the value represents just a single host.

Small Demonstration:
Create a sample table:

CREATE TABLE tbl_TestNetworkDataType
(
	ID INT
	,MyIPAddress INET
	,MyMACAddress MACADDR
);

Insert few sample Network related records:

INSERT INTO tbl_TestNetworkDataType
VALUES 
(1,'10.0.2.8/16','08008b:010803')
,(2,'192.168.1.0/24','08:00:2b:01:02:03')
,(3,'150.155.124.0/32','0800.2b01.0203')
,(4,'08.26/16','08002b:010203');

Check the inserted data:

SELECT *FROM tbl_TestNetworkDataType;

 id |  myipaddress   |   mymacaddress
----+----------------+-------------------
  1 | 10.0.2.8/16    | 08:00:8b:01:08:03
  2 | 192.168.1.0/24 | 08:00:2b:01:02:03
  3 | 150.155.124.0  | 08:00:2b:01:02:03
  4 | 8.26.0.0/16    | 08:00:2b:01:02:03

In this post, I am sharing a demonstration on how to validate the range of IP Address in SQL Server.

You can set CHECK CONSTRAINT for each part of IP Address for validating a proper range.

For example,
You require inserting IP Address between 10.20 range. This you can achieve using PARSENAME function of SQL Server.

Below is a full demo on this:

Let’s first create one table and define CHECK Constraint using PARSENAME.

CREATE TABLE tbl_IPAddress
(
 IPAddress VARCHAR(15)
)
GO

ALTER TABLE tbl_IPAddress ADD CONSTRAINT chk_tbl_IPAddress_IPAddress
CHECK 
(
 (ParseName(IPAddress, 4) = 12) 
 AND (ParseName(IPAddress, 3) = 4) 
 AND (ParseName(IPAddress, 2) BETWEEN 8 AND 26) 
 AND (ParseName(IPAddress, 1) BETWEEN 1 AND 255) 
)
GO

You can see different four part validation ,

First two part validation is: only IP Address range start with 12.4

Last two part validation is: 8 to 26 and 1 to 255.

Means valid IP Address are :

12.4.8.125

12.4.15.241

Invalid IP Address are:

10.2.21.52

12.4.7.124

Now insert script for some valid IP Address:

INSERT INTO tbl_IPAddress  (IPAddress) 
VALUES 
        ('12.4.8.34')
        ,('12.4.16.125')
        ,('12.4.22.120')
        ,('12.4.22.120')
        ,('12.4.15.216')
GO

If you tried to insert out of range, then this will show you an error that you cannot violate check constraint.

Script to Select different part of stored IP Address:

SELECT IPAddress
     ,ParseName(IPAddress, 4) As FirstPart
     ,ParseName(IPAddress, 3) As SecondPart
     ,ParseName(IPAddress, 2) As ThirdPart
     ,ParseName(IPAddress, 1) As FourthPart
FROM   tbl_IPAddress

My Suggestion:

In this demo, I stored IP Address into one VARCHAR(15) column which is not effective storage.
Whenever you don’t require any analysis on IP Address, then you can store the IP Address into one column. Otherwise, please visit this page on the effective storage of IP Addresses.

In this post, I am sharing about the effective storage of IP-Address into Database System.

Now let’s talk about four part of IP-Address.

E.g, 152.145.10.25

Many database developers or database designer store this IP-Address into one column which is VARCHAR(15).

What do you think? Is this effective storage of IP-Address?.

Now imagine that you are playing with 10,0,00,00 online customers in which all this IP-Address of the customer requires for analysis.

If we stored all IP-Addresses into one column, you have to perform string manipulation for finding a particular range of IP-Address.
The string operation is always costly and not advisable.

Effective storage of IP-Address is very simple:

Just divide your full-length IP-Address into four part.

E.g.

Full IP-Address: 152.145.10.25

Four Part :

152

145

10

25

Now create four tinyint/smallint column to store this four different part.

column like,

ip1 tinyint

ip2 tinyint

ip3 tinyint

ip4 tinyint

The full IP-Address split into four different integer part.

Now the task is very easy:
You can also apply an index on all this part and perform range analysis very quickly.

Yes, I agree that during insertion you also require splitting for storing in the different columns, but this is only a one time process after that you can easily use different parts for various analysis.

During select, you can also concat this four part and make full IP-Address for display purpose.