Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
418 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 133 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. #16863720 | C2 | semidirect |
| 3. #16863720 | C2 | semidirect |
| 4. #16863714 | C2 | semidirect |
| 5. #16863709 | C2 | semidirect |
| 6. #16863436 | C2 | semidirect |
| 7. #16863432 | C2 | semidirect |
| 8. #16863400 | C2 | semidirect |
| 9. C2×#14523963 | C2 | semidirect |
| 10. #16863363 | C2 | semidirect |
| 11. #520×C67 | C2 | semidirect |
| 21. #14523976 | C22 | semidirect |
| 22. #14523976 | C22 | semidirect |
| 23. #14523976 | C22 | semidirect |
| 24. #14523974 | C22 | semidirect |
| 25. #14523974 | C22 | semidirect |
| 26. #14523974 | C22 | semidirect |
| 31. C22⋊(C67⋊C8) | C22 | semidirect |
| 32. C22⋊(C67⋊C8) | C22 | semidirect |
| 38. #117×C67 | C22 | semidirect |
| 40. C2×C4⋊C4×C67 | C22 | semidirect |
| 135. C67 | #3096 | semidirect |
| 137. #520 | D67 | semidirect |
| 161. #117 | C2×D67 | semidirect |
| 163. C2×C4⋊C4 | C2×D67 | semidirect |