Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
496 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
| 2. C2×M16×D53 | C2 | semidirect |
| 4. C2×#13133193 | C2 | semidirect |
| 5. #16810880 | C2 | semidirect |
| 6. #16810872 | C2 | semidirect |
| 7. #16810863 | C2 | semidirect |
| 8. #16810855 | C2 | semidirect |
| 9. #16810666 | C2 | semidirect |
| 10. #16810625 | C2 | semidirect |
| 11. C53×#419 | C2 | semidirect |
| 15. C2×#11719925 | C22 | semidirect |
| 16. C2×#11719924 | C22 | semidirect |
| 36. #13133150 | C22 | semidirect |
| 37. #13133148 | C22 | semidirect |
| 38. #13133142 | C22 | semidirect |
| 39. #13133139 | C22 | semidirect |
| 43. #103×C53 | C22 | semidirect |
| 44. #103×C53 | C22 | semidirect |
| 88. #11719917 | D4 | semidirect |
| 145. C2×D53 | #137 | semidirect |
| 173. #419 | D53 | semidirect |
| 175. C53 | #3056 | semidirect |
| 206. #103 | C2×D53 | semidirect |
| 207. #103 | C2×D53 | semidirect |