Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#13133239 | C2 | semidirect |
| 2. #16811294 | C2 | semidirect |
| 3. #16811278 | C2 | semidirect |
| 4. #16810996 | C2 | semidirect |
| 5. #16810852 | C2 | semidirect |
| 6. #16810834 | C2 | semidirect |
| 7. #16810819 | C2 | semidirect |
| 8. #16810787 | C2 | semidirect |
| 9. #16810770 | C2 | semidirect |
| 10. C4×#11719913 | C2 | semidirect |
| 11. C8×D4×C53 | C2 | semidirect |
| 81. #11719913 | D4 | semidirect |
| 127. C4×C53 | #135 | semidirect |
| 151. C8×D4 | D53 | semidirect |
| 152. C53 | #3284 | semidirect |
| 272. C4 | #13133239 | semidirect |