Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
| 3. #16811001 | C2 | semidirect |
| 4. #16810864 | C2 | semidirect |
| 5. #16810861 | C2 | semidirect |
| 6. #16810831 | C2 | semidirect |
| 7. #16810779 | C2 | semidirect |
| 8. #16810777 | C2 | semidirect |
| 9. Q16×Dic53 | C2 | semidirect |
| 11. C22×Q16×C53 | C2 | semidirect |
| 57. Q16×C53 | D4 | semidirect |
| 94. C22⋊D53 | Q16 | direct (N × H) |
| 112. C22×C53 | C2×Q16 | semidirect |
| 116. C2×D53 | C2×Q16 | semidirect |
| 126. Dic53 | C2×Q16 | semidirect |
| 134. C22×Q16 | D53 | semidirect |
| 144. C53 | D4×Q16 | semidirect |
| 193. Q16 | C22⋊D53 | direct (N × H) |
| 248. C22 | Q16×D53 | semidirect |