Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
444 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 129 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. #16863673 | C2 | semidirect |
| 4. #16863598 | C2 | semidirect |
| 6. #16863494 | C2 | semidirect |
| 7. #16863453 | C2 | semidirect |
| 8. #533×C67 | C2 | semidirect |
| 18. #14523976 | C22 | semidirect |
| 19. C4⋊(C67⋊C8) | C22 | semidirect |
| 20. #14523967 | C22 | semidirect |
| 23. #14523954 | C22 | semidirect |
| 24. C4⋊Q8×C67 | C22 | semidirect |
| 25. C4⋊Q8×C67 | C22 | semidirect |
| 30. C4×Q8×C67 | C22 | semidirect |
| 113. C67 | #3110 | semidirect |
| 114. #533 | D67 | semidirect |
| 125. C4⋊Q8 | C2×D67 | semidirect |
| 126. C4⋊Q8 | C2×D67 | semidirect |
| 131. C4×Q8 | C2×D67 | semidirect |