My DNS flow:
[root@sonar ~]# nslookup 192.168.1.68
Server: 192.168.1.5
Address: 192.168.1.5#53

** server can't find 68.1.168.192.in-addr.arpa.: NXDOMAIN

[root@sonar ~]# nslookup sonar.girmiti.com
Server: 192.168.1.5
Address: 192.168.1.5#53
My /etc/named.conf
** server can't find sonar.girmiti.com: NXDOMAIN
//
// named.conf
//
// Provided by Red Hat bind package to configure the ISC BIND named(8) DNS
// server as a caching only nameserver (as a localhost DNS resolver only).
//
// See /usr/share/doc/bind*/sample/ for example named configuration files.
//

options {
listen-on port 53 { 127.0.0.1; 192.168.1.68;};
listen-on-v6 port 53 { ::1; };
directory "/var/named";
dump-file "/var/named/data/cache_dump.db";
statistics-file "/var/named/data/named_stats.txt";
memstatistics-file "/var/named/data/named_mem_stats.txt";
allow-query { localhost;192.168.1.0/19; };
recursion yes;

dnssec-enable yes;
dnssec-validation yes;

/* Path to ISC DLV key */
bindkeys-file "/etc/named.iscdlv.key";

managed-keys-directory "/var/named/dynamic";
};

logging {
channel default_debug {
file "data/named.run";
severity dynamic;
};
};

zone "." IN {
type hint;
file "named.ca";
};

include "/etc/named.rfc1912.zones";
include "/etc/named.root.key";
My rfc1912 file:
zone "girmiti.com" IN {
type master;
file "sonar.flz";
allow-update { none; };
};


zone "1.168.192.in-addr.arpa" IN {
type master;
file "sonar.rlz";
allow-update { none; };
};

My /etc/hosts & /etc/network:
default 192.168.1.2
loopback 127.0.0.0
link-local 169.254.0.0

127.0.0.1 localhost localhost.localdomain localhost4 localhost4.localdomain4
::1 localhost localhost.localdomain localhost6 localhost6.localdomain6

192.168.1.68 sonar.girmiti.com sonar

My rlz:
$TTL 86400
@ IN SOA sonar.girmiti.com. root.sonar.girmiti.com. (
2014051001 ; serial
3600 ; refresh
1800 ; retry
604800 ; expire
86400 ; minimum

)

@ IN NS sonar.girmiti.com.
@ IN PTR girmiti.com.
sonar A 192.168.1.68

My Flz:

$TTL 86400
@ IN SOA sonar.girmiti.com. root.sonar.girmiti.com. (
2014051001 ; serial
3600 ; refresh
1800 ; retry
604800 ; expire
86400 ; minimum

)

@ IN NS sonar.girmiti.com.
@ IN A 192.168.1.68
sonar A 192.168.1.68

dig -x 192.168.1.68

; <<>> DiG 9.8.2rc1-RedHat-9.8.2-0.68.rc1.el6 <<>> -x 192.168.1.68
;; global options: +cmd
;; Got answer:
;; ->>HEADER<<- opcode: QUERY, status: NXDOMAIN, id: 18905
;; flags: qr aa rd ra; QUERY: 1, ANSWER: 0, AUTHORITY: 1, ADDITIONAL: 0

;; QUESTION SECTION:
;68.1.168.192.in-addr.arpa. IN PTR

;; AUTHORITY SECTION:
168.192.in-addr.arpa. 10800 IN SOA localhost. nobody.invalid. 1 3600 1200 604800 10800

;; Query time: 2 msec
;; SERVER: 192.168.1.5#53(192.168.1.5)
;; WHEN: Wed Jul 18 15:27:08 2018
;; MSG SIZE rcvd: 102

dig sonar.girmiti.com

; <<>> DiG 9.8.2rc1-RedHat-9.8.2-0.68.rc1.el6 <<>> sonar.girmiti.com
;; global options: +cmd
;; Got answer:
;; ->>HEADER<<- opcode: QUERY, status: NXDOMAIN, id: 45441
;; flags: qr rd ra; QUERY: 1, ANSWER: 0, AUTHORITY: 1, ADDITIONAL: 0

;; QUESTION SECTION:
;sonar.girmiti.com. IN A

;; AUTHORITY SECTION:
girmiti.com. 355 IN SOA ns1.bizmailserver.net. abuse.bizmailserver.net.girmiti.com. 2018052201 10800 3600 604800 600

;; Query time: 1 msec
;; SERVER: 192.168.1.5#53(192.168.1.5)
;; WHEN: Wed Jul 18 15:27:50 2018
;; MSG SIZE rcvd: 116

Kindly I request all to solve this issue, I am unable to solve this issue.

Unless 192.168.1.5 has a dns server on it, you need to check your resolv.conf to see where dns queries go to. Your problem can be translated to: Internal network cannot resolve (External)internet names.

Where's your dns server?

You can't just invent a subdomain and add it to some other name server

The authorative name servers for girmiti.com are NS1.BIZMAILSERVER.NET and NS2.BIZMAILSERVER.NET
That's where you'll need to add the subdomain of sonar.

Thanks for the reply,could you please suggest me for how to add the subdomains in the DNS please?

Contact the administrators of bizmailserver.net?

yes it's our server only. We have already contacted.

So your question is solved?