Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#11761615 | C2 | semidirect |
| 3. #16863870 | C2 | semidirect |
| 4. #16863608 | C2 | semidirect |
| 5. #16863598 | C2 | semidirect |
| 6. #16863423 | C2 | semidirect |
| 7. #16863405 | C2 | semidirect |
| 8. #16863392 | C2 | semidirect |
| 9. #536×C67 | C2 | semidirect |
| 22. C4⋊(C67⋊C8) | C22 | semidirect |
| 23. #14523967 | C22 | semidirect |
| 24. #14523967 | C22 | semidirect |
| 25. #14523964 | C22 | semidirect |
| 28. C4⋊Q8×C67 | C22 | semidirect |
| 29. #124×C67 | C22 | semidirect |
| 117. C67 | #3042 | semidirect |
| 120. #536 | D67 | semidirect |
| 137. C4⋊Q8 | C2×D67 | semidirect |
| 138. #124 | C2×D67 | semidirect |