42 groups of order 688.
| SmallGroups | group |
|---|---|
| (688, 1) | C43⋊C16 #10621869 |
| (688, 2) | C16×C43 #10621870 |
| (688, 3) | C8×D43 #10621871 |
| (688, 4) | #10621872 |
| (688, 5) | #10621873 |
| (688, 6) | D344 #10621874 |
| (688, 7) | Dic172 #10621875 |
| (688, 8) | C2×C43⋊C8 #10621876 |
| (688, 9) | #10621877 |
| (688, 10) | C4×Dic43 #10621878 |
| (688, 11) | Dic43⋊C4 #10621879 |
| (688, 12) | C4⋊Dic43 #10621880 |
| (688, 13) | (C2×D43)⋊C4 #10621881 |
| (688, 14) | #10621882 |
| (688, 15) | #10621883 |
| (688, 16) | #10621884 |
| (688, 17) | #10621885 |
| (688, 18) | C22⋊Dic43 #10621886 |
| (688, 19) | C42×C43 #10621887 |
| (688, 20) | C22⋊C4×C43 #10621888 |
| (688, 21) | C4⋊C4×C43 #10621889 |
| (688, 22) | C2×C8×C43 #10621890 |
| (688, 23) | M16×C43 #10621891 |
| (688, 24) | D8×C43 #10621892 |
| (688, 25) | SD16×C43 #10621893 |
| (688, 26) | Q16×C43 #10621894 |
| (688, 27) | C2×Dic86 #10621895 |
| (688, 28) | C2×C4×D43 #10621896 |
| (688, 29) | C2×D172 #10621897 |
| (688, 30) | #10621898 |
| (688, 31) | D4×D43 #10621899 |
| (688, 32) | #10621900 |
| (688, 33) | Q8×D43 #10621901 |
| (688, 34) | #10621902 |
| (688, 35) | C22×Dic43 #10621903 |
| (688, 36) | C2×C22⋊D43 #10621904 |
| (688, 37) | C22×C4×C43 #10621905 |
| (688, 38) | C2×D4×C43 #10621906 |
| (688, 39) | C2×Q8×C43 #10621907 |
| (688, 40) | #41×C43 #10621908 |
| (688, 41) | C23×D43 #10621909 |
| (688, 42) | C24×C43 #10621910 |