Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
738 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13133248 | C2 | semidirect |
| 3. #16810779 | C2 | semidirect |
| 4. #16810762 | C2 | semidirect |
| 5. #16810632 | C2 | semidirect |
| 6. #16810587 | C2 | semidirect |
| 7. C23×Q8×C53 | C2 | semidirect |
| 10. C2×#11719925 | C22 | semidirect |
| 11. C2×#11719924 | C22 | semidirect |
| 19. #13133141 | C22 | semidirect |
| 35. C2×Q8×C53 | D4 | semidirect |
| 93. C22×C53 | #137 | semidirect |
| 109. C23×Q8 | D53 | semidirect |
| 116. C53 | #3004 | semidirect |
| 146. C2×Q8 | C22⋊D53 | semidirect |
| 204. C22 | #13133248 | semidirect |