Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
546 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 546 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 |
|---|---|---|
| 1. C2×#14524068 | C2 | semidirect |
| 2. D4×D268 | C2 | semidirect |
| 3. #16863770 | C2 | semidirect |
| 4. #16863644 | C2 | semidirect |
| 5. #16863598 | C2 | semidirect |
| 6. #16863591 | C2 | semidirect |
| 7. #16863546 | C2 | semidirect |
| 8. #16863541 | C2 | semidirect |
| 9. C4×#11761613 | C2 | semidirect |
| 10. #16863474 | C2 | semidirect |
| 11. #547×C67 | C2 | semidirect |
| 16. C2×#11761615 | C22 | semidirect |
| 17. C2×#11761615 | C22 | semidirect |
| 19. C2×#11761613 | C22 | semidirect |
| 20. C2×#11761612 | C22 | semidirect |
| 26. #14523976 | C22 | semidirect |
| 27. C4⋊(C67⋊C8) | C22 | semidirect |
| 28. #14523967 | C22 | semidirect |
| 29. #14523964 | C22 | semidirect |
| 31. #14523963 | C22 | semidirect |
| 32. C22⋊(C67⋊C8) | C22 | semidirect |
| 33. C4×C67⋊C8 | C22 | semidirect |
| 34. C2×#41×C67 | C22 | semidirect |
| 35. C4⋊Q8×C67 | C22 | semidirect |
| 37. C22⋊Q8×C67 | C22 | semidirect |
| 40. C4×D4×C67 | C22 | semidirect |
| 57. #11761613 | D4 | semidirect |
| 95. D4×C67 | C2×D4 | semidirect |
| 118. C67⋊C8 | C2×D4 | semidirect |
| 137. C4×C67 | AGL(1,ℤ/8) | semidirect |
| 149. C67 | #3272 | semidirect |
| 151. #547 | D67 | semidirect |
| 161. C2×#41 | C2×D67 | semidirect |
| 171. C4⋊Q8 | C2×D67 | semidirect |
| 174. C22⋊Q8 | C2×D67 | semidirect |
| 181. C4×D4 | C2×D67 | semidirect |
| 252. D4 | D4×D67 | semidirect |
| 287. C4 | #14524068 | semidirect |