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×#13133237 | C2 | semidirect |
| 2. #16811278 | C2 | semidirect |
| 3. #16810995 | C2 | semidirect |
| 4. #16810850 | C2 | semidirect |
| 5. #16810833 | C2 | semidirect |
| 6. #16810815 | C2 | semidirect |
| 7. #16810785 | C2 | semidirect |
| 8. #16810766 | C2 | semidirect |
| 9. C4×#11719924 | C2 | semidirect |
| 10. D4×#88322 | C2 | semidirect |
| 11. C53×#550 | C2 | semidirect |
| 69. #11719924 | D4 | semidirect |
| 129. C4×C53 | #135 | semidirect |
| 142. #550 | D53 | semidirect |
| 152. C53 | #3284 | semidirect |
| 272. C4 | #13133237 | semidirect |