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Elements of the group are displayed as permutations of degree 17.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 3P | ||||||
| $(S_3\times D_6^2).S_4$ | 1A | $1$ | $1$ | $(S_3\times D_6^2).S_4$ | 1A | 1A | $()$ |
| $(S_3\times D_6^2).S_4$ | 2A | $2$ | $3$ | $C_3^3.C_2^6.C_2^2$ | 1A | 2A | $(10,13)(11,12)(14,15)(16,17)$ |
| $(S_3\times D_6^2).S_4$ | 2B | $2$ | $6$ | $C_3^3.C_2^6.C_2$ | 1A | 2B | $(10,14)(11,17)(12,16)(13,15)$ |
| $(S_3\times D_6^2).S_4$ | 2C | $2$ | $6$ | $C_3^3.C_2^6.C_2$ | 1A | 2C | $(11,16)(12,17)$ |
| $(S_3\times D_6^2).S_4$ | 2D | $2$ | $27$ | $(C_2^2\times D_{12}):D_4$ | 1A | 2D | $(2,6)(5,7)$ |
| $(S_3\times D_6^2).S_4$ | 2E | $2$ | $27$ | $(C_2^2\times D_{12}):D_4$ | 1A | 2E | $(1,7)(4,8)(10,15)(11,17)(12,16)(13,14)$ |
| $(S_3\times D_6^2).S_4$ | 2F | $2$ | $36$ | $D_6^2:C_2^2$ | 1A | 2F | $(6,9)(10,11)(12,13)(14,16)(15,17)$ |
| $(S_3\times D_6^2).S_4$ | 2G | $2$ | $54$ | $C_2^5.D_6$ | 1A | 2G | $(5,7)(6,9)(11,12)(16,17)$ |
| $(S_3\times D_6^2).S_4$ | 2H | $2$ | $54$ | $C_2^5:D_6$ | 1A | 2H | $(5,7)(6,9)(10,14)(11,16)(12,17)(13,15)$ |
| $(S_3\times D_6^2).S_4$ | 2I | $2$ | $54$ | $C_2^4:D_{12}$ | 1A | 2I | $(3,4)(5,7)(10,13)(11,16)(12,17)(14,15)$ |
| $(S_3\times D_6^2).S_4$ | 2J | $2$ | $72$ | $D_6^2:C_2$ | 1A | 2J | $(2,8)(3,9)(4,6)(12,17)(13,15)$ |
| $(S_3\times D_6^2).S_4$ | 2K | $2$ | $108$ | not computed | 1A | 2K | $(4,8)(5,7)(6,9)(10,12)(11,13)(14,17)(15,16)$ |
| $(S_3\times D_6^2).S_4$ | 2L | $2$ | $108$ | not computed | 1A | 2L | $(1,5)(3,8)(10,15)(11,16)(12,17)(13,14)$ |
| $(S_3\times D_6^2).S_4$ | 2M | $2$ | $108$ | not computed | 1A | 2M | $(4,8)(6,9)(11,12)(16,17)$ |
| $(S_3\times D_6^2).S_4$ | 2N | $2$ | $216$ | not computed | 1A | 2N | $(1,5)(2,8)(3,6)(4,9)(10,11)(12,15)(13,17)(14,16)$ |
| $(S_3\times D_6^2).S_4$ | 3A | $3$ | $6$ | $C_3^2.(C_2^4\times C_6).C_2^2$ | 3A | 1A | $(3,8,4)$ |
| $(S_3\times D_6^2).S_4$ | 3B | $3$ | $8$ | $C_2^4:\He_3.C_6$ | 3B | 1A | $(1,7,5)(2,9,6)(3,8,4)$ |
| $(S_3\times D_6^2).S_4$ | 3C | $3$ | $12$ | $C_6^3.C_2^3$ | 3C | 1A | $(2,9,6)(3,8,4)$ |
| $(S_3\times D_6^2).S_4$ | 3D | $3$ | $1152$ | not computed | 3D | 1A | $(1,3,2)(4,6,5)(7,8,9)(10,13,14)(11,17,12)$ |
| $(S_3\times D_6^2).S_4$ | 4A | $4$ | $36$ | $D_6^2.C_2^2$ | 2A | 4A | $(6,9)(10,17,15,11)(12,13,16,14)$ |
| $(S_3\times D_6^2).S_4$ | 4B | $4$ | $72$ | $C_2.D_6^2$ | 2A | 4B | $(6,9)(10,12,13,11)(14,17,15,16)$ |
| $(S_3\times D_6^2).S_4$ | 4C | $4$ | $72$ | $D_{12}:D_6$ | 2A | 4C | $(2,8)(3,9)(4,6)(10,15,14,13)(11,17,16,12)$ |
| $(S_3\times D_6^2).S_4$ | 4D | $4$ | $144$ | not computed | 2C | 4D | $(1,2)(5,6)(7,9)(11,17,12,16)(14,15)$ |
| $(S_3\times D_6^2).S_4$ | 4E | $4$ | $216$ | not computed | 2E | 4E | $(1,8,7,4)(3,5)(10,12,15,16)(11,13,17,14)$ |
| $(S_3\times D_6^2).S_4$ | 4F | $4$ | $216$ | not computed | 2A | 4F | $(1,6)(2,5)(3,8)(7,9)(10,12,13,11)(14,16,15,17)$ |
| $(S_3\times D_6^2).S_4$ | 4G | $4$ | $216$ | not computed | 2D | 4G | $(1,3)(4,7,8,5)(10,12)(11,14)(13,17)(15,16)$ |
| $(S_3\times D_6^2).S_4$ | 4H | $4$ | $324$ | not computed | 2A | 4H | $(2,6)(4,8)(5,7)(10,12,15,16)(11,14,17,13)$ |
| $(S_3\times D_6^2).S_4$ | 4I | $4$ | $432$ | not computed | 2B | 4I | $(1,2)(3,8)(5,6)(7,9)(10,12,14,16)(11,15,17,13)$ |
| $(S_3\times D_6^2).S_4$ | 4J | $4$ | $432$ | not computed | 2I | 4J | $(1,8)(3,7,4,5)(10,12,13,17)(11,15,16,14)$ |
| $(S_3\times D_6^2).S_4$ | 4K | $4$ | $648$ | not computed | 2D | 4K | $(1,9)(2,7,6,5)(3,4)(11,12)(14,15)$ |
| $(S_3\times D_6^2).S_4$ | 4L | $4$ | $648$ | not computed | 2E | 4L | $(1,4)(2,6)(3,5,8,7)(10,13,15,14)(11,12,17,16)$ |
| $(S_3\times D_6^2).S_4$ | 4M | $4$ | $1296$ | not computed | 2G | 4M | $(1,3)(2,6)(4,5,8,7)(11,12,17,16)(13,14)$ |
| $(S_3\times D_6^2).S_4$ | 6A | $6$ | $6$ | $C_3^2.(C_2^4\times C_6).C_2^2$ | 3A | 2A | $(3,8,4)(10,13)(11,12)(14,15)(16,17)$ |
| $(S_3\times D_6^2).S_4$ | 6B | $6$ | $12$ | $(C_2\times C_6^3):C_4$ | 3A | 2B | $(3,4,8)(10,14)(11,17)(12,16)(13,15)$ |
| $(S_3\times D_6^2).S_4$ | 6C | $6$ | $12$ | $C_6^3.C_2^3$ | 3A | 2A | $(3,8,4)(10,14)(11,16)(12,17)(13,15)$ |
| $(S_3\times D_6^2).S_4$ | 6D | $6$ | $12$ | $C_6^3.C_2^3$ | 3C | 2A | $(2,6,9)(3,8,4)(10,14)(11,16)(12,17)(13,15)$ |
| $(S_3\times D_6^2).S_4$ | 6E | $6$ | $12$ | $C_6^3.C_2^3$ | 3A | 2C | $(3,8,4)(11,12)(16,17)$ |
| $(S_3\times D_6^2).S_4$ | 6F | $6$ | $24$ | $C_6^3:C_2^2$ | 3A | 2C | $(3,4,8)(11,16)(12,17)$ |
| $(S_3\times D_6^2).S_4$ | 6G | $6$ | $24$ | $C_6^3:C_2^2$ | 3A | 2B | $(3,4,8)(10,13)(11,16)(12,17)(14,15)$ |
| $(S_3\times D_6^2).S_4$ | 6H | $6$ | $24$ | $C_6^3.C_2^2$ | 3C | 2B | $(1,5,7)(2,6,9)(10,14)(11,17)(12,16)(13,15)$ |
| $(S_3\times D_6^2).S_4$ | 6I | $6$ | $24$ | $C_6^3.C_2^2$ | 3C | 2C | $(1,5,7)(2,6,9)(10,13)(14,15)$ |
| $(S_3\times D_6^2).S_4$ | 6J | $6$ | $24$ | $C_6^3.C_2^2$ | 3C | 2A | $(1,5,7)(3,8,4)(10,14)(11,16)(12,17)(13,15)$ |
| $(S_3\times D_6^2).S_4$ | 6K | $6$ | $24$ | $C_6^3.C_2^2$ | 3B | 2A | $(1,7,5)(2,9,6)(3,8,4)(10,15)(11,17)(12,16)(13,14)$ |
| $(S_3\times D_6^2).S_4$ | 6L1 | $6$ | $24$ | $C_6^3.C_2^2$ | 3B | 2C | $(1,7,5)(2,6,9)(3,4,8)(11,12)(16,17)$ |
| $(S_3\times D_6^2).S_4$ | 6L-1 | $6$ | $24$ | $C_6^3.C_2^2$ | 3B | 2C | $(1,5,7)(2,9,6)(3,8,4)(11,12)(16,17)$ |
| $(S_3\times D_6^2).S_4$ | 6M | $6$ | $48$ | $C_2\times C_6^3$ | 3C | 2C | $(2,6,9)(3,4,8)(11,12)(16,17)$ |
| $(S_3\times D_6^2).S_4$ | 6N | $6$ | $48$ | $C_2\times C_6^3$ | 3C | 2B | $(2,6,9)(3,4,8)(10,13)(11,16)(12,17)(14,15)$ |
| $(S_3\times D_6^2).S_4$ | 6O | $6$ | $48$ | $C_2\times C_6^3$ | 3B | 2B | $(1,5,7)(2,6,9)(3,4,8)(10,13)(11,16)(12,17)(14,15)$ |
| $(S_3\times D_6^2).S_4$ | 6P | $6$ | $54$ | $C_3\times C_2^4:D_4$ | 3A | 2E | $(1,7)(2,6,9)(4,8)(10,15)(11,17)(12,16)(13,14)$ |
| $(S_3\times D_6^2).S_4$ | 6Q | $6$ | $54$ | $C_3\times C_2^4:D_4$ | 3A | 2D | $(2,6,9)(4,8)(5,7)$ |