Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
414 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 414 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 |
|---|---|---|
| 2. C2×#14524001 | C2 | semidirect |
| 3. #16863736 | C2 | semidirect |
| 4. #16863735 | C2 | semidirect |
| 5. #16863719 | C2 | semidirect |
| 6. #16863718 | C2 | semidirect |
| 7. #16863438 | C2 | semidirect |
| 8. #16863436 | C2 | semidirect |
| 9. #16863397 | C2 | semidirect |
| 10. #16863359 | C2 | semidirect |
| 11. #417×C67 | C2 | semidirect |
| 30. #14523977 | C22 | semidirect |
| 31. #14523976 | C22 | semidirect |
| 32. #14523975 | C22 | semidirect |
| 33. #14523974 | C22 | semidirect |
| 34. #14523967 | C22 | semidirect |
| 35. #14523964 | C22 | semidirect |
| 41. #103×C67 | C22 | semidirect |
| 42. #102×C67 | C22 | semidirect |
| 153. C67 | #3093 | semidirect |
| 163. #417 | D67 | semidirect |
| 191. #103 | C2×D67 | semidirect |
| 193. #102 | C2×D67 | semidirect |