Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
458 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 123 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×C4⋊C4×D67 | C2 | semidirect |
| 3. #16863730 | C2 | semidirect |
| 4. #16863724 | C2 | semidirect |
| 5. #16863716 | C2 | semidirect |
| 6. #16863710 | C2 | semidirect |
| 7. #16863709 | C2 | semidirect |
| 8. #16863435 | C2 | semidirect |
| 9. #16863396 | C2 | semidirect |
| 10. #16863358 | C2 | semidirect |
| 11. #483×C67 | C2 | semidirect |
| 30. #14523977 | C22 | semidirect |
| 31. #14523976 | C22 | semidirect |
| 32. #14523974 | C22 | semidirect |
| 33. #14523967 | C22 | semidirect |
| 34. #14523965 | C22 | semidirect |
| 35. #14523963 | C22 | semidirect |
| 40. #106×C67 | C22 | semidirect |
| 41. #103×C67 | C22 | semidirect |
| 147. C67 | #3092 | semidirect |
| 152. #483 | D67 | semidirect |
| 182. #106 | C2×D67 | semidirect |
| 184. #103 | C2×D67 | semidirect |