Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
492 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 200 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 |
|---|---|---|
| 2. #16811634 | C2 | semidirect |
| 3. #16811633 | C2 | semidirect |
| 12. #13133286 | C22 | semidirect |
| 13. #13133285 | C22 | semidirect |
| 15. C2×#11719917 | C4 | semidirect |
| 16. C2×#11719912 | C4 | semidirect |
| 17. M16×D53 | C4 | semidirect |
| 20. C2×M16×C53 | C4 | semidirect |
| 39. M16×C53 | C2×C4 | semidirect |
| 40. C2×C8×C53 | C2×C4 | semidirect |
| 41. #11719917 | C2×C4 | semidirect |
| 42. C2×#88322 | C2×C4 | semidirect |
| 43. #11719912 | C2×C4 | semidirect |
| 44. C8×D53 | C2×C4 | semidirect |
| 102. C53 | #2911 | semidirect |
| 108. C2×M16 | #6157 | semidirect |
| 133. M16 | C2×#6157 | semidirect |
| 137. C2×C8 | C2×#6157 | semidirect |