15 groups of order 686.
| SmallGroups | group |
|---|---|
| (686, 1) | D343 #10621852 |
| (686, 2) | C2×C343 #10621853 |
| (686, 3) | C7×D49 #10621854 |
| (686, 4) | D7×C49 #10621855 |
| (686, 5) | (C7⋊D7)⋊C7 #10621856 |
| (686, 6) | D49⋊C7 #10621857 |
| (686, 7) | C7⋊D49 #10621858 |
| (686, 8) | #10621859 |
| (686, 9) | C2×C7×C49 #10621860 |
| (686, 10) | C2×H(3,𝔽7) #10621861 |
| (686, 11) | C2×7−1+2 #10621862 |
| (686, 12) | C72×D7 #10621863 |
| (686, 13) | C7×C7⋊D7 #10621864 |
| (686, 14) | C7⋊(C7⋊D7) #10621865 |
| (686, 15) | C2×C73 #10621866 |