Elements of the group are displayed as permutations of degree 14.
| Group |
Label |
Order |
Size |
Centralizer |
Powers |
Representative |
| 2P |
3P |
| $C_2\times A_4^2:D_4$ |
1A |
$1$ |
$1$ |
$C_2\times A_4^2:D_4$ |
1A |
1A |
$()$ |
| $C_2\times A_4^2:D_4$ |
2A |
$2$ |
$1$ |
$C_2\times A_4^2:D_4$ |
1A |
2A |
$(13,14)$ |
| $C_2\times A_4^2:D_4$ |
2B |
$2$ |
$1$ |
$C_2\times A_4^2:D_4$ |
1A |
2B |
$(9,12)(10,11)$ |
| $C_2\times A_4^2:D_4$ |
2C |
$2$ |
$1$ |
$C_2\times A_4^2:D_4$ |
1A |
2C |
$(9,12)(10,11)(13,14)$ |
| $C_2\times A_4^2:D_4$ |
2D |
$2$ |
$2$ |
$C_2^3\times A_4^2$ |
1A |
2D |
$(10,11)$ |
| $C_2\times A_4^2:D_4$ |
2E |
$2$ |
$2$ |
$C_2^3\times A_4^2$ |
1A |
2E |
$(10,11)(13,14)$ |
| $C_2\times A_4^2:D_4$ |
2F |
$2$ |
$6$ |
$A_4\times C_2^5$ |
1A |
2F |
$(3,4)(5,6)$ |
| $C_2\times A_4^2:D_4$ |
2G |
$2$ |
$6$ |
$A_4\times C_2^5$ |
1A |
2G |
$(3,4)(5,6)(13,14)$ |
| $C_2\times A_4^2:D_4$ |
2H |
$2$ |
$6$ |
$A_4\times C_2^5$ |
1A |
2H |
$(3,4)(5,6)(10,11)$ |
| $C_2\times A_4^2:D_4$ |
2I |
$2$ |
$6$ |
$A_4\times C_2^5$ |
1A |
2I |
$(3,4)(5,6)(10,11)(13,14)$ |
| $C_2\times A_4^2:D_4$ |
2J |
$2$ |
$6$ |
$A_4\times C_2^5$ |
1A |
2J |
$(3,4)(5,6)(9,12)$ |
| $C_2\times A_4^2:D_4$ |
2K |
$2$ |
$6$ |
$A_4\times C_2^5$ |
1A |
2K |
$(3,4)(5,6)(9,12)(13,14)$ |
| $C_2\times A_4^2:D_4$ |
2L |
$2$ |
$6$ |
$A_4\times C_2^5$ |
1A |
2L |
$(3,4)(5,6)(9,12)(10,11)$ |
| $C_2\times A_4^2:D_4$ |
2M |
$2$ |
$6$ |
$A_4\times C_2^5$ |
1A |
2M |
$(3,4)(5,6)(9,12)(10,11)(13,14)$ |
| $C_2\times A_4^2:D_4$ |
2N |
$2$ |
$9$ |
$C_2^5:D_4$ |
1A |
2N |
$(1,2)(3,4)(5,6)(7,8)(13,14)$ |
| $C_2\times A_4^2:D_4$ |
2O |
$2$ |
$9$ |
$C_2^5:D_4$ |
1A |
2O |
$(1,2)(3,4)(5,6)(7,8)(9,12)(10,11)(13,14)$ |
| $C_2\times A_4^2:D_4$ |
2P |
$2$ |
$9$ |
$C_2^5:D_4$ |
1A |
2P |
$(1,7)(2,8)(3,5)(4,6)$ |
| $C_2\times A_4^2:D_4$ |
2Q |
$2$ |
$9$ |
$C_2^5:D_4$ |
1A |
2Q |
$(1,2)(3,5)(4,6)(7,8)(9,12)(10,11)$ |
| $C_2\times A_4^2:D_4$ |
2R |
$2$ |
$18$ |
$C_2^7$ |
1A |
2R |
$(1,2)(3,4)(5,6)(7,8)(10,11)$ |
| $C_2\times A_4^2:D_4$ |
2S |
$2$ |
$18$ |
$C_2^7$ |
1A |
2S |
$(1,2)(3,4)(5,6)(7,8)(10,11)(13,14)$ |
| $C_2\times A_4^2:D_4$ |
2T |
$2$ |
$24$ |
$C_2^3\times A_4$ |
1A |
2T |
$(1,3)(2,4)(5,7)(6,8)(9,10)(11,12)(13,14)$ |
| $C_2\times A_4^2:D_4$ |
2U |
$2$ |
$24$ |
$C_2^3\times A_4$ |
1A |
2U |
$(1,6)(2,5)(3,8)(4,7)(9,10)(11,12)$ |
| $C_2\times A_4^2:D_4$ |
3A1 |
$3$ |
$8$ |
$C_2^3:C_6^2$ |
3A-1 |
1A |
$(4,6,5)$ |
| $C_2\times A_4^2:D_4$ |
3A-1 |
$3$ |
$8$ |
$C_2^3:C_6^2$ |
3A1 |
1A |
$(4,5,6)$ |
| $C_2\times A_4^2:D_4$ |
3B1 |
$3$ |
$16$ |
$C_6^2:C_2^2$ |
3B-1 |
1A |
$(2,8,7)(4,6,5)$ |
| $C_2\times A_4^2:D_4$ |
3B-1 |
$3$ |
$16$ |
$C_6^2:C_2^2$ |
3B1 |
1A |
$(2,7,8)(4,5,6)$ |
| $C_2\times A_4^2:D_4$ |
3C |
$3$ |
$32$ |
$C_2\times C_6^2$ |
3C |
1A |
$(2,8,7)(4,5,6)$ |
| $C_2\times A_4^2:D_4$ |
4A |
$4$ |
$24$ |
$C_2^3:C_{12}$ |
2B |
4A |
$(1,6)(2,4)(3,7)(5,8)(9,11,12,10)(13,14)$ |
| $C_2\times A_4^2:D_4$ |
4B |
$4$ |
$24$ |
$C_2^3:C_{12}$ |
2B |
4B |
$(1,5)(2,4)(3,8)(6,7)(9,10,12,11)$ |
| $C_2\times A_4^2:D_4$ |
4C |
$4$ |
$72$ |
$C_2^3\times C_4$ |
2P |
4C |
$(1,4,7,6)(2,3,8,5)(9,11)(10,12)(13,14)$ |
| $C_2\times A_4^2:D_4$ |
4D |
$4$ |
$72$ |
$C_2^3\times C_4$ |
2P |
4D |
$(1,5,8,3)(2,4,7,6)(9,11)(10,12)$ |
| $C_2\times A_4^2:D_4$ |
4E |
$4$ |
$72$ |
$C_2^3\times C_4$ |
2Q |
4E |
$(1,3,2,5)(4,7,6,8)(9,11,12,10)$ |
| $C_2\times A_4^2:D_4$ |
4F |
$4$ |
$72$ |
$C_2^3\times C_4$ |
2Q |
4F |
$(1,4,7,3)(2,5,8,6)(9,11,12,10)(13,14)$ |
| $C_2\times A_4^2:D_4$ |
6A1 |
$6$ |
$8$ |
$C_2^3:C_6^2$ |
3A1 |
2A |
$(4,5,6)(13,14)$ |
| $C_2\times A_4^2:D_4$ |
6A-1 |
$6$ |
$8$ |
$C_2^3:C_6^2$ |
3A-1 |
2A |
$(4,6,5)(13,14)$ |
| $C_2\times A_4^2:D_4$ |
6B1 |
$6$ |
$8$ |
$C_2^3:C_6^2$ |
3A1 |
2D |
$(4,5,6)(10,11)$ |
| $C_2\times A_4^2:D_4$ |
6B-1 |
$6$ |
$8$ |
$C_2^3:C_6^2$ |
3A-1 |
2D |
$(4,6,5)(10,11)$ |
| $C_2\times A_4^2:D_4$ |
6C1 |
$6$ |
$8$ |
$C_2^3:C_6^2$ |
3A1 |
2E |
$(4,5,6)(10,11)(13,14)$ |
| $C_2\times A_4^2:D_4$ |
6C-1 |
$6$ |
$8$ |
$C_2^3:C_6^2$ |
3A-1 |
2E |
$(4,6,5)(10,11)(13,14)$ |
| $C_2\times A_4^2:D_4$ |
6D1 |
$6$ |
$8$ |
$C_2^3:C_6^2$ |
3A1 |
2D |
$(4,5,6)(9,12)$ |
| $C_2\times A_4^2:D_4$ |
6D-1 |
$6$ |
$8$ |
$C_2^3:C_6^2$ |
3A-1 |
2D |
$(4,6,5)(9,12)$ |
| $C_2\times A_4^2:D_4$ |
6E1 |
$6$ |
$8$ |
$C_2^3:C_6^2$ |
3A1 |
2E |
$(4,5,6)(9,12)(13,14)$ |
| $C_2\times A_4^2:D_4$ |
6E-1 |
$6$ |
$8$ |
$C_2^3:C_6^2$ |
3A-1 |
2E |
$(4,6,5)(9,12)(13,14)$ |
| $C_2\times A_4^2:D_4$ |
6F1 |
$6$ |
$8$ |
$C_2^3:C_6^2$ |
3A1 |
2B |
$(4,5,6)(9,12)(10,11)$ |
| $C_2\times A_4^2:D_4$ |
6F-1 |
$6$ |
$8$ |
$C_2^3:C_6^2$ |
3A-1 |
2B |
$(4,6,5)(9,12)(10,11)$ |
| $C_2\times A_4^2:D_4$ |
6G1 |
$6$ |
$8$ |
$C_2^3:C_6^2$ |
3A1 |
2C |
$(4,5,6)(9,12)(10,11)(13,14)$ |
| $C_2\times A_4^2:D_4$ |
6G-1 |
$6$ |
$8$ |
$C_2^3:C_6^2$ |
3A-1 |
2C |
$(4,6,5)(9,12)(10,11)(13,14)$ |
| $C_2\times A_4^2:D_4$ |
6H1 |
$6$ |
$16$ |
$C_6^2:C_2^2$ |
3B1 |
2A |
$(2,7,8)(4,5,6)(13,14)$ |
| $C_2\times A_4^2:D_4$ |
6H-1 |
$6$ |
$16$ |
$C_6^2:C_2^2$ |
3B-1 |
2A |
$(2,8,7)(4,6,5)(13,14)$ |
| $C_2\times A_4^2:D_4$ |
6I1 |
$6$ |
$16$ |
$C_6^2:C_2^2$ |
3B1 |
2C |
$(2,7,8)(4,5,6)(9,12)(10,11)(13,14)$ |
