Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
404 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 141 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. #16811352 | C2 | semidirect |
| 3. #16810996 | C2 | semidirect |
| 4. #16810829 | C2 | semidirect |
| 5. #16810824 | C2 | semidirect |
| 6. C4×#11719913 | C2 | semidirect |
| 7. C8×Q8×C53 | C2 | semidirect |
| 45. Q8×C53 | SD16 | semidirect |
| 60. C8×C53 | #41 | semidirect |
| 82. C8×Q8 | D53 | semidirect |
| 84. C53 | #3392 | semidirect |
| 124. Q8 | #11719913 | semidirect |
| 137. C8 | #11719949 | semidirect |