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. #16811003 | C2 | semidirect |
| 4. #16810865 | C2 | semidirect |
| 5. #16810833 | C2 | semidirect |
| 6. #16810780 | C2 | semidirect |
| 8. C4×Q16×C53 | C2 | semidirect |
| 37. Q16×C53 | D4 | semidirect |
| 65. D212 | Q16 | direct (N × H) |
| 78. C2×D53 | C2×Q16 | semidirect |
| 82. C4×C53 | C2×Q16 | semidirect |
| 98. C4×Q16 | D53 | semidirect |
| 100. C53 | D4×Q16 | semidirect |
| 132. Q16 | D212 | direct (N × H) |
| 176. C4 | Q16×D53 | semidirect |