Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 125 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. #16811277 | C2 | semidirect |
| 2. #16810969 | C2 | semidirect |
| 3. #16810939 | C2 | semidirect |
| 4. #16810908 | C2 | semidirect |
| 5. #16810874 | C2 | semidirect |
| 6. #16810815 | C2 | semidirect |
| 7. #16810768 | C2 | semidirect |
| 8. C4×#11719924 | C2 | semidirect |
| 9. #16810701 | C2 | semidirect |
| 10. #16810624 | C2 | semidirect |
| 11. C53×#550 | C2 | semidirect |
| 81. Q8×C53 | #41 | semidirect |
| 135. #550 | D53 | semidirect |
| 146. C53 | #3332 | semidirect |
| 217. Q8 | #11719947 | semidirect |