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Elements of the group are displayed as permutations of degree 15.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 3P | ||||||
| $(D_4\times C_2^3).D_6^2$ | 1A | $1$ | $1$ | not computed | 1A | 1A | $()$ |
| $(D_4\times C_2^3).D_6^2$ | 2A | $2$ | $1$ | not computed | 1A | 2A | $(8,15)(9,10)(11,13)(12,14)$ |
| $(D_4\times C_2^3).D_6^2$ | 2B | $2$ | $2$ | not computed | 1A | 2B | $(9,10)(11,13)$ |
| $(D_4\times C_2^3).D_6^2$ | 2C | $2$ | $3$ | not computed | 1A | 2C | $(4,6)(5,7)$ |
| $(D_4\times C_2^3).D_6^2$ | 2D | $2$ | $3$ | not computed | 1A | 2D | $(4,6)(5,7)(8,15)(9,10)(11,13)(12,14)$ |
| $(D_4\times C_2^3).D_6^2$ | 2E | $2$ | $4$ | not computed | 1A | 2E | $(11,13)(12,14)$ |
| $(D_4\times C_2^3).D_6^2$ | 2F | $2$ | $4$ | not computed | 1A | 2F | $(8,12)(9,11)(10,13)(14,15)$ |
| $(D_4\times C_2^3).D_6^2$ | 2G | $2$ | $6$ | not computed | 1A | 2G | $(4,6)(5,7)(9,10)(11,13)$ |
| $(D_4\times C_2^3).D_6^2$ | 2H | $2$ | $8$ | not computed | 1A | 2H | $(9,11)(10,13)(12,14)$ |
| $(D_4\times C_2^3).D_6^2$ | 2I | $2$ | $8$ | not computed | 1A | 2I | $(8,9)(10,15)(11,12)(13,14)$ |
| $(D_4\times C_2^3).D_6^2$ | 2J | $2$ | $12$ | not computed | 1A | 2J | $(2,3)(12,14)$ |
| $(D_4\times C_2^3).D_6^2$ | 2K | $2$ | $12$ | not computed | 1A | 2K | $(2,3)(9,10)(11,13)(12,14)$ |
| $(D_4\times C_2^3).D_6^2$ | 2L | $2$ | $12$ | not computed | 1A | 2L | $(2,3)(9,11)(10,13)$ |
| $(D_4\times C_2^3).D_6^2$ | 2M | $2$ | $12$ | not computed | 1A | 2M | $(2,3)(8,12)(9,10)(11,13)(14,15)$ |
| $(D_4\times C_2^3).D_6^2$ | 2N | $2$ | $12$ | not computed | 1A | 2N | $(4,6)(5,7)(8,12)(9,13)(10,11)(14,15)$ |
| $(D_4\times C_2^3).D_6^2$ | 2O | $2$ | $12$ | not computed | 1A | 2O | $(4,7)(5,6)(8,15)(9,10)$ |
| $(D_4\times C_2^3).D_6^2$ | 2P | $2$ | $18$ | not computed | 1A | 2P | $(2,3)(6,7)$ |
| $(D_4\times C_2^3).D_6^2$ | 2Q | $2$ | $18$ | not computed | 1A | 2Q | $(2,3)(6,7)(8,15)(9,10)(11,13)(12,14)$ |
| $(D_4\times C_2^3).D_6^2$ | 2R | $2$ | $24$ | not computed | 1A | 2R | $(6,7)(12,14)$ |
| $(D_4\times C_2^3).D_6^2$ | 2S | $2$ | $24$ | not computed | 1A | 2S | $(6,7)(9,10)(11,13)(12,14)$ |
| $(D_4\times C_2^3).D_6^2$ | 2T | $2$ | $24$ | not computed | 1A | 2T | $(6,7)(9,11)(10,13)$ |
| $(D_4\times C_2^3).D_6^2$ | 2U | $2$ | $24$ | not computed | 1A | 2U | $(6,7)(8,12)(9,10)(11,13)(14,15)$ |
| $(D_4\times C_2^3).D_6^2$ | 2V | $2$ | $24$ | not computed | 1A | 2V | $(4,5)(6,7)(9,11)(10,13)(12,14)$ |
| $(D_4\times C_2^3).D_6^2$ | 2W | $2$ | $24$ | not computed | 1A | 2W | $(4,5)(6,7)(8,9)(10,15)(11,12)(13,14)$ |
| $(D_4\times C_2^3).D_6^2$ | 2X | $2$ | $36$ | not computed | 1A | 2X | $(2,3)(6,7)(9,10)(11,13)$ |
| $(D_4\times C_2^3).D_6^2$ | 2Y | $2$ | $36$ | not computed | 1A | 2Y | $(2,3)(4,5)(6,7)(12,14)$ |
| $(D_4\times C_2^3).D_6^2$ | 2Z | $2$ | $36$ | not computed | 1A | 2Z | $(2,3)(4,5)(6,7)(9,10)(11,13)(12,14)$ |
| $(D_4\times C_2^3).D_6^2$ | 2AA | $2$ | $36$ | not computed | 1A | 2AA | $(2,3)(4,5)(6,7)(9,11)(10,13)$ |
| $(D_4\times C_2^3).D_6^2$ | 2AB | $2$ | $36$ | not computed | 1A | 2AB | $(2,3)(4,5)(6,7)(8,12)(9,10)(11,13)(14,15)$ |
| $(D_4\times C_2^3).D_6^2$ | 2AC | $2$ | $72$ | not computed | 1A | 2AC | $(2,3)(6,7)(11,13)(12,14)$ |
| $(D_4\times C_2^3).D_6^2$ | 2AD | $2$ | $72$ | not computed | 1A | 2AD | $(2,3)(6,7)(8,12)(9,11)(10,13)(14,15)$ |
| $(D_4\times C_2^3).D_6^2$ | 2AE | $2$ | $144$ | not computed | 1A | 2AE | $(2,3)(6,7)(8,12)(11,13)(14,15)$ |
| $(D_4\times C_2^3).D_6^2$ | 2AF | $2$ | $144$ | not computed | 1A | 2AF | $(1,2)(6,7)(8,9)(10,15)(11,12)(13,14)$ |
| $(D_4\times C_2^3).D_6^2$ | 3A | $3$ | $2$ | not computed | 3A | 1A | $(1,3,2)$ |
| $(D_4\times C_2^3).D_6^2$ | 3B | $3$ | $8$ | not computed | 3B | 1A | $(5,7,6)$ |
| $(D_4\times C_2^3).D_6^2$ | 3C | $3$ | $16$ | not computed | 3C | 1A | $(1,3,2)(5,7,6)$ |
| $(D_4\times C_2^3).D_6^2$ | 4A | $4$ | $4$ | not computed | 2B | 4A | $(9,13,10,11)$ |
| $(D_4\times C_2^3).D_6^2$ | 4B | $4$ | $4$ | not computed | 2B | 4B | $(8,14,15,12)(9,10)(11,13)$ |
| $(D_4\times C_2^3).D_6^2$ | 4C | $4$ | $4$ | not computed | 2A | 4C | $(8,14,15,12)(9,11,10,13)$ |
| $(D_4\times C_2^3).D_6^2$ | 4D | $4$ | $8$ | not computed | 2A | 4D | $(8,10,15,9)(11,14,13,12)$ |
| $(D_4\times C_2^3).D_6^2$ | 4E | $4$ | $12$ | not computed | 2B | 4E | $(4,5)(6,7)(9,13,10,11)$ |
| $(D_4\times C_2^3).D_6^2$ | 4F | $4$ | $12$ | not computed | 2B | 4F | $(4,5)(6,7)(8,14,15,12)(9,10)(11,13)$ |
| $(D_4\times C_2^3).D_6^2$ | 4G | $4$ | $12$ | not computed | 2A | 4G | $(4,5)(6,7)(8,14,15,12)(9,13,10,11)$ |
| $(D_4\times C_2^3).D_6^2$ | 4H | $4$ | $18$ | not computed | 2C | 4H | $(2,3)(4,5,6,7)$ |
| $(D_4\times C_2^3).D_6^2$ | 4I | $4$ | $18$ | not computed | 2C | 4I | $(2,3)(4,5,6,7)(8,15)(9,10)(11,13)(12,14)$ |
| $(D_4\times C_2^3).D_6^2$ | 4J | $4$ | $24$ | not computed | 2A | 4J | $(4,5)(6,7)(8,10,15,9)(11,14,13,12)$ |
| $(D_4\times C_2^3).D_6^2$ | 4K | $4$ | $24$ | not computed | 2C | 4K | $(4,7,6,5)(12,14)$ |
| $(D_4\times C_2^3).D_6^2$ | 4L | $4$ | $24$ | not computed | 2C | 4L | $(4,7,6,5)(9,10)(11,13)(12,14)$ |
| $(D_4\times C_2^3).D_6^2$ | 4M | $4$ | $24$ | not computed | 2C | 4M | $(4,7,6,5)(9,11)(10,13)$ |
| $(D_4\times C_2^3).D_6^2$ | 4N | $4$ | $24$ | not computed | 2C | 4N | $(4,7,6,5)(8,12)(9,10)(11,13)(14,15)$ |