Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 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 |
|---|---|---|
| 2. #16863729 | C2 | semidirect |
| 3. #16863709 | C2 | semidirect |
| 4. #16863644 | C2 | semidirect |
| 5. #16863546 | C2 | semidirect |
| 6. #16863535 | C2 | semidirect |
| 7. #16863360 | C2 | semidirect |
| 8. C2×C22⋊Q8×C67 | C2 | semidirect |
| 11. C2×#11761615 | C22 | semidirect |
| 12. C2×#11761612 | C22 | semidirect |
| 19. #14523976 | C22 | semidirect |
| 20. #14523967 | C22 | semidirect |
| 21. #14523963 | C22 | semidirect |
| 23. C22⋊(C67⋊C8) | C22 | semidirect |
| 24. C22×Q8×C67 | C22 | semidirect |
| 29. C22⋊Q8×C67 | C22 | semidirect |
| 31. C2×C4⋊C4×C67 | C22 | semidirect |
| 130. C67 | #3193 | semidirect |
| 131. C2×C22⋊Q8 | D67 | semidirect |
| 139. C22×Q8 | C2×D67 | semidirect |
| 148. C22⋊Q8 | C2×D67 | semidirect |
| 155. C2×C4⋊C4 | C2×D67 | semidirect |