Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 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. #16811274 | C2 | semidirect |
| 2. #16811027 | C2 | semidirect |
| 3. #16810938 | C2 | semidirect |
| 4. #16810936 | C2 | semidirect |
| 5. #16810902 | C2 | semidirect |
| 6. #16810860 | C2 | semidirect |
| 7. #16810859 | C2 | semidirect |
| 8. #16810705 | C2 | semidirect |
| 9. C8×C22⋊D53 | C2 | semidirect |
| 10. #107×D53 | C2 | semidirect |
| 11. C2×#107×C53 | C2 | semidirect |
| 81. C22⋊D53 | D8 | semidirect |
| 95. C8×C53 | #41 | semidirect |
| 134. C2×#107 | D53 | semidirect |
| 135. C53 | #3334 | semidirect |
| 221. C8 | #11719945 | semidirect |