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×#13133238 | C2 | semidirect |
| 2. #16811295 | C2 | semidirect |
| 3. #16811277 | C2 | semidirect |
| 4. #16810996 | C2 | semidirect |
| 5. #16810853 | C2 | semidirect |
| 6. #16810833 | C2 | semidirect |
| 7. #16810818 | C2 | semidirect |
| 8. #16810788 | C2 | semidirect |
| 9. #16810769 | C2 | semidirect |
| 10. C8×D212 | C2 | semidirect |
| 11. C4×SD16×C53 | C2 | semidirect |
| 60. SD16×C53 | D4 | semidirect |
| 129. C4×C53 | #135 | semidirect |
| 150. C4×SD16 | D53 | semidirect |
| 152. C53 | #3284 | semidirect |
| 204. SD16 | D212 | semidirect |
| 272. C4 | #13133238 | semidirect |