Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 450 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 |
|---|---|---|
| 1. C2×C4×D268 | C2 | semidirect |
| 2. #16863724 | C2 | semidirect |
| 3. #16863707 | C2 | semidirect |
| 4. #16863693 | C2 | semidirect |
| 5. #16863608 | C2 | semidirect |
| 6. #16863546 | C2 | semidirect |
| 8. #16863506 | C2 | semidirect |
| 9. #16863494 | C2 | semidirect |
| 10. #16863453 | C2 | semidirect |
| 11. #529×C67 | C2 | semidirect |
| 22. #14523976 | C22 | semidirect |
| 23. #14523974 | C22 | semidirect |
| 24. C4⋊(C67⋊C8) | C22 | semidirect |
| 25. #14523967 | C22 | semidirect |
| 26. #14523964 | C22 | semidirect |
| 31. #14523954 | C22 | semidirect |
| 33. #125×C67 | C22 | semidirect |
| 34. #124×C67 | C22 | semidirect |
| 38. C4×Q8×C67 | C22 | semidirect |
| 40. C4×D4×C67 | C22 | semidirect |
| 141. C67 | #3114 | semidirect |
| 142. #529 | D67 | semidirect |
| 158. #125 | C2×D67 | semidirect |
| 159. #124 | C2×D67 | semidirect |
| 163. C4×Q8 | C2×D67 | semidirect |
| 169. C4×D4 | C2×D67 | semidirect |