Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
352 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 352 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. #16864106 | C2 | semidirect |
| 2. #16863801 | C2 | semidirect |
| 3. #16863798 | C2 | semidirect |
| 4. #16863697 | C2 | semidirect |
| 5. #16863687 | C2 | semidirect |
| 8. C8×Q8×C67 | C2 | semidirect |
| 32. D536 | Q8 | semidirect |
| 82. C67 | #3380 | semidirect |
| 88. C8×Q8 | D67 | semidirect |