Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #16863740 | C2 | semidirect |
| 4. #16863739 | C2 | semidirect |
| 5. #16863733 | C2 | semidirect |
| 6. #16863728 | C2 | semidirect |
| 7. #16863439 | C2 | semidirect |
| 8. #16863404 | C2 | semidirect |
| 9. C2×#14523968 | C2 | semidirect |
| 11. #427×C67 | C2 | semidirect |
| 127. C67 | #3097 | semidirect |
| 135. #427 | D67 | semidirect |