Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
448 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 448 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. #16863744 | C2 | semidirect |
| 3. #16863720 | C2 | semidirect |
| 4. #16863673 | C2 | semidirect |
| 5. #16863644 | C2 | semidirect |
| 6. #16863596 | C2 | semidirect |
| 7. #16863546 | C2 | semidirect |
| 8. C4×#11761615 | C2 | semidirect |
| 9. #16863474 | C2 | semidirect |
| 10. #16863400 | C2 | semidirect |
| 11. #556×C67 | C2 | semidirect |
| 15. C2×#11761615 | C22 | semidirect |
| 16. C2×#11761612 | C22 | semidirect |
| 22. #14523976 | C22 | semidirect |
| 23. #14523974 | C22 | semidirect |
| 24. C4⋊(C67⋊C8) | C22 | semidirect |
| 25. #14523967 | C22 | semidirect |
| 28. #14523963 | C22 | semidirect |
| 29. #14523963 | C22 | semidirect |
| 30. #14523963 | C22 | semidirect |
| 31. C22⋊(C67⋊C8) | C22 | semidirect |
| 32. C4×C67⋊C8 | C22 | semidirect |
| 33. C4⋊Q8×C67 | C22 | semidirect |
| 36. C22⋊Q8×C67 | C22 | semidirect |
| 38. C4×Q8×C67 | C22 | semidirect |
| 40. #117×C67 | C22 | semidirect |
| 136. C67 | #3324 | semidirect |
| 137. #556 | D67 | semidirect |
| 153. C4⋊Q8 | C2×D67 | semidirect |
| 157. C22⋊Q8 | C2×D67 | semidirect |
| 162. C4×Q8 | C2×D67 | semidirect |
| 165. #117 | C2×D67 | semidirect |