Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
216 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 65 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. #16863447 | C2 | semidirect |
| 3. #16863418 | C2 | semidirect |
| 4. Q8⋊(C67⋊C8) | C2 | semidirect |
| 5. #16863125 | C2 | semidirect |
| 6. #16863123 | C2 | semidirect |
| 7. Q8⋊C8×C67 | C2 | semidirect |
| 106. C67 | #1495 | semidirect |
| 111. Q8⋊C8 | D67 | semidirect |