Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 123 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. #16811346 | C2 | semidirect |
| 2. #16811005 | C2 | semidirect |
| 3. #16810995 | C2 | semidirect |
| 4. #16810842 | C2 | semidirect |
| 5. #16810838 | C2 | semidirect |
| 6. #16810833 | C2 | semidirect |
| 8. Q8×#88322 | C2 | semidirect |
| 9. C4×#11719924 | C2 | semidirect |
| 10. C4×#11719923 | C2 | semidirect |
| 11. C53×#559 | C2 | semidirect |
| 126. #559 | D53 | semidirect |
| 137. C53 | #3394 | semidirect |