Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 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×#14524031 | C2 | semidirect |
| 2. #16863783 | C2 | semidirect |
| 3. #16863758 | C2 | semidirect |
| 4. #16863611 | C2 | semidirect |
| 5. #16863534 | C2 | semidirect |
| 6. #16863529 | C2 | semidirect |
| 7. #16863453 | C2 | semidirect |
| 8. #532×C67 | C2 | semidirect |
| 11. C2×#11761616 | C22 | semidirect |
| 19. C4⋊(C67⋊C8) | C22 | semidirect |
| 20. #14523966 | C22 | semidirect |
| 23. #14523954 | C22 | semidirect |
| 25. C4⋊Q8×C67 | C22 | semidirect |
| 26. #127×C67 | C22 | semidirect |
| 31. C4×D4×C67 | C22 | semidirect |
| 121. C67 | #3213 | semidirect |
| 122. #532 | D67 | semidirect |
| 135. C4⋊Q8 | C2×D67 | semidirect |
| 136. #127 | C2×D67 | semidirect |
| 145. C4×D4 | C2×D67 | semidirect |