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Elements of the group are displayed as words in the presentation $\langle a, b, c, d \mid a^{2}=c^{28}=d^{12}=[a,b]=[a,d]=1, b^{2}=d^{6}, c^{a}=c^{27}d^{6}, c^{b}=cd^{3}, d^{b}=d^{11}, d^{c}=d^{7} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 7P
$(C_3\times D_{14}):Q_{16}$ 1A $1$ $1$ $(C_3\times D_{14}):Q_{16}$ 1A 1A 1A $1$
$(C_3\times D_{14}):Q_{16}$ 2A $2$ $1$ $(C_3\times D_{14}):Q_{16}$ 1A 2A 2A $d^{6}$
$(C_3\times D_{14}):Q_{16}$ 2B $2$ $1$ $(C_3\times D_{14}):Q_{16}$ 1A 2B 2B $c^{14}d^{6}$
$(C_3\times D_{14}):Q_{16}$ 2C $2$ $1$ $(C_3\times D_{14}):Q_{16}$ 1A 2C 2C $c^{14}$
$(C_3\times D_{14}):Q_{16}$ 2D $2$ $14$ $C_6.C_2^4$ 1A 2D 2D $a$
$(C_3\times D_{14}):Q_{16}$ 2E $2$ $14$ $C_6.C_2^4$ 1A 2E 2E $ad^{6}$
$(C_3\times D_{14}):Q_{16}$ 3A $3$ $2$ $C_{12}.D_{28}$ 3A 1A 3A $d^{8}$
$(C_3\times D_{14}):Q_{16}$ 4A $4$ $2$ $C_{12}.D_{28}$ 2A 4A 4A $c^{14}d^{9}$
$(C_3\times D_{14}):Q_{16}$ 4B $4$ $2$ $C_{12}.D_{28}$ 2A 4B 4B $d^{9}$
$(C_3\times D_{14}):Q_{16}$ 4C $4$ $8$ $C_2\times C_{84}$ 2C 4C 4C $c^{21}$
$(C_3\times D_{14}):Q_{16}$ 4D $4$ $12$ $C_4\times D_{14}$ 2A 4D 4D $bd^{6}$
$(C_3\times D_{14}):Q_{16}$ 4E $4$ $12$ $C_4\times D_{14}$ 2A 4E 4E $bc^{14}d^{6}$
$(C_3\times D_{14}):Q_{16}$ 4F $4$ $28$ $C_2^2\times C_{12}$ 2A 4F 4F $ad^{3}$
$(C_3\times D_{14}):Q_{16}$ 4G $4$ $56$ $C_2\times C_{12}$ 2A 4G 4G $ac^{27}d^{9}$
$(C_3\times D_{14}):Q_{16}$ 4H $4$ $84$ $C_2^2\times C_4$ 2A 4H 4H $abc^{4}$
$(C_3\times D_{14}):Q_{16}$ 4I $4$ $84$ $C_2^2\times C_4$ 2A 4I 4I $abd^{5}$
$(C_3\times D_{14}):Q_{16}$ 6A $6$ $2$ $C_{12}.D_{28}$ 3A 2A 6A $d^{2}$
$(C_3\times D_{14}):Q_{16}$ 6B $6$ $2$ $C_{12}.D_{28}$ 3A 2B 6B $c^{14}d^{2}$
$(C_3\times D_{14}):Q_{16}$ 6C $6$ $2$ $C_{12}.D_{28}$ 3A 2C 6C $c^{14}d^{8}$
$(C_3\times D_{14}):Q_{16}$ 6D $6$ $28$ $C_2^2\times C_{12}$ 3A 2D 6D $ad^{4}$
$(C_3\times D_{14}):Q_{16}$ 6E $6$ $28$ $C_2^2\times C_{12}$ 3A 2E 6E $ad^{2}$
$(C_3\times D_{14}):Q_{16}$ 7A1 $7$ $2$ $C_{28}.D_{12}$ 7A2 7A3 1A $c^{16}$
$(C_3\times D_{14}):Q_{16}$ 7A2 $7$ $2$ $C_{28}.D_{12}$ 7A3 7A1 1A $c^{4}$
$(C_3\times D_{14}):Q_{16}$ 7A3 $7$ $2$ $C_{28}.D_{12}$ 7A1 7A2 1A $c^{20}$
$(C_3\times D_{14}):Q_{16}$ 8A1 $8$ $12$ $C_2\times C_{56}$ 4A 8A3 8A1 $bc^{7}d^{9}$
$(C_3\times D_{14}):Q_{16}$ 8A3 $8$ $12$ $C_2\times C_{56}$ 4A 8A1 8A3 $bc^{21}d^{6}$
$(C_3\times D_{14}):Q_{16}$ 8B1 $8$ $84$ $C_2\times C_8$ 4B 8B3 8B1 $abcd^{4}$
$(C_3\times D_{14}):Q_{16}$ 8B3 $8$ $84$ $C_2\times C_8$ 4B 8B1 8B3 $abcd$
$(C_3\times D_{14}):Q_{16}$ 12A $12$ $4$ $C_{12}\times D_{14}$ 6A 4B 12A $d^{7}$
$(C_3\times D_{14}):Q_{16}$ 12B $12$ $4$ $C_{12}\times D_{14}$ 6A 4A 12B $c^{14}d^{7}$
$(C_3\times D_{14}):Q_{16}$ 12C1 $12$ $8$ $C_2\times C_{84}$ 6C 4C 12C1 $c^{7}d^{4}$
$(C_3\times D_{14}):Q_{16}$ 12C-1 $12$ $8$ $C_2\times C_{84}$ 6C 4C 12C-1 $c^{21}d^{8}$
$(C_3\times D_{14}):Q_{16}$ 12D1 $12$ $28$ $C_2^2\times C_{12}$ 6A 4F 12D5 $ad$
$(C_3\times D_{14}):Q_{16}$ 12D5 $12$ $28$ $C_2^2\times C_{12}$ 6A 4F 12D1 $ad^{5}$
$(C_3\times D_{14}):Q_{16}$ 12E1 $12$ $56$ $C_2\times C_{12}$ 6A 4G 12E1 $ac^{27}d^{7}$
$(C_3\times D_{14}):Q_{16}$ 12E-1 $12$ $56$ $C_2\times C_{12}$ 6A 4G 12E-1 $ac^{27}d^{5}$
$(C_3\times D_{14}):Q_{16}$ 14A1 $14$ $2$ $C_{28}.D_{12}$ 7A1 14A3 2A $c^{8}d^{6}$
$(C_3\times D_{14}):Q_{16}$ 14A3 $14$ $2$ $C_{28}.D_{12}$ 7A3 14A5 2A $c^{24}d^{6}$
$(C_3\times D_{14}):Q_{16}$ 14A5 $14$ $2$ $C_{28}.D_{12}$ 7A2 14A1 2A $c^{12}d^{6}$
$(C_3\times D_{14}):Q_{16}$ 14B1 $14$ $2$ $C_{28}.D_{12}$ 7A1 14B3 2B $c^{6}d^{6}$
$(C_3\times D_{14}):Q_{16}$ 14B3 $14$ $2$ $C_{28}.D_{12}$ 7A3 14B5 2B $c^{18}d^{6}$
$(C_3\times D_{14}):Q_{16}$ 14B5 $14$ $2$ $C_{28}.D_{12}$ 7A2 14B1 2B $c^{2}d^{6}$
$(C_3\times D_{14}):Q_{16}$ 14C1 $14$ $2$ $C_{28}.D_{12}$ 7A1 14C3 2C $c^{6}$
$(C_3\times D_{14}):Q_{16}$ 14C3 $14$ $2$ $C_{28}.D_{12}$ 7A3 14C5 2C $c^{18}$
$(C_3\times D_{14}):Q_{16}$ 14C5 $14$ $2$ $C_{28}.D_{12}$ 7A2 14C1 2C $c^{2}$
$(C_3\times D_{14}):Q_{16}$ 21A1 $21$ $4$ $C_4:C_{84}$ 21A2 7A1 3A $c^{4}d^{4}$
$(C_3\times D_{14}):Q_{16}$ 21A2 $21$ $4$ $C_4:C_{84}$ 21A4 7A2 3A $c^{8}d^{8}$
$(C_3\times D_{14}):Q_{16}$ 21A4 $21$ $4$ $C_4:C_{84}$ 21A1 7A3 3A $c^{16}d^{4}$
$(C_3\times D_{14}):Q_{16}$ 28A1 $28$ $4$ $C_6:C_{56}$ 14A3 28A3 4A $c^{2}d^{3}$
$(C_3\times D_{14}):Q_{16}$ 28A3 $28$ $4$ $C_6:C_{56}$ 14A5 28A5 4A $c^{6}d^{9}$
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