Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
482 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 131 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×Q16×D53 | C2 | semidirect |
| 2. #16811280 | C2 | semidirect |
| 3. #16811006 | C2 | semidirect |
| 4. #16810864 | C2 | semidirect |
| 5. #16810856 | C2 | semidirect |
| 6. #16810843 | C2 | semidirect |
| 7. #16810785 | C2 | semidirect |
| 8. #16810760 | C2 | semidirect |
| 9. Q16×Dic53 | C2 | semidirect |
| 10. C8×C22⋊D53 | C2 | semidirect |
| 11. C2×#135×C53 | C2 | semidirect |
| 56. Q16×C53 | D4 | semidirect |
| 120. C2×D53 | #135 | semidirect |
| 137. C2×#135 | D53 | semidirect |
| 148. C53 | #3285 | semidirect |
| 195. Q16 | C22⋊D53 | semidirect |