Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
370 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 117 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. #16811228 | C2 | semidirect |
| 2. #16810923 | C2 | semidirect |
| 3. #16810920 | C2 | semidirect |
| 4. #16810874 | C2 | semidirect |
| 5. #16810857 | C2 | semidirect |
| 6. #16810818 | C2 | semidirect |
| 7. #16810815 | C2 | semidirect |
| 8. #16810650 | C2 | semidirect |
| 9. C53×#540 | C2 | semidirect |
| 108. #540 | D53 | semidirect |
| 116. C53 | #3259 | semidirect |