Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
462 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 137 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. #16863714 | C2 | semidirect |
| 4. #16863709 | C2 | semidirect |
| 5. #16863439 | C2 | semidirect |
| 6. #16863400 | C2 | semidirect |
| 7. #16863360 | C2 | semidirect |
| 8. C2×#117×C67 | C2 | semidirect |
| 18. #14523976 | C22 | semidirect |
| 19. #14523974 | C22 | semidirect |
| 20. #14523963 | C22 | semidirect |
| 21. #14523963 | C22 | semidirect |
| 22. C22⋊(C67⋊C8) | C22 | semidirect |
| 23. C22⋊(C67⋊C8) | C22 | semidirect |
| 28. #117×C67 | C22 | semidirect |
| 29. C2×C4⋊C4×C67 | C22 | semidirect |
| 30. C2×C4⋊C4×C67 | C22 | semidirect |
| 126. C67 | #3094 | semidirect |
| 128. C2×#117 | D67 | semidirect |
| 146. #117 | C2×D67 | semidirect |
| 148. C2×C4⋊C4 | C2×D67 | semidirect |
| 149. C2×C4⋊C4 | C2×D67 | semidirect |