Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
338 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 338 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 |
|---|---|---|
| 2. #16863795 | C2 | semidirect |
| 3. #16863792 | C2 | semidirect |
| 4. #16863703 | C2 | semidirect |
| 6. #16863691 | C2 | semidirect |
| 8. Q8×C67⋊C8 | C2 | semidirect |
| 11. #557×C67 | C2 | semidirect |
| 45. #11761615 | Q8 | semidirect |
| 115. C67 | #3381 | semidirect |
| 116. #557 | D67 | semidirect |