Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
410 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 127 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. #16863436 | C2 | semidirect |
| 8. #16863406 | C2 | semidirect |
| 9. #16863404 | C2 | semidirect |
| 11. #428×C67 | C2 | semidirect |
| 30. #14523976 | C22 | semidirect |
| 31. #14523974 | C22 | semidirect |
| 32. #14523968 | C22 | semidirect |
| 33. #14523968 | C22 | semidirect |
| 34. #14523966 | C22 | semidirect |
| 35. #14523966 | C22 | semidirect |
| 41. #107×C67 | C22 | semidirect |
| 42. #106×C67 | C22 | semidirect |
| 147. C67 | #3095 | semidirect |
| 155. #428 | D67 | semidirect |
| 181. #107 | C2×D67 | semidirect |
| 183. #106 | C2×D67 | semidirect |