Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 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. #16863693 | C2 | semidirect |
| 3. #16863693 | C2 | semidirect |
| 4. #16863683 | C2 | semidirect |
| 5. #16863673 | C2 | semidirect |
| 6. #16863436 | C2 | semidirect |
| 7. #16863432 | C2 | semidirect |
| 8. #16863423 | C2 | semidirect |
| 11. #544×C67 | C2 | semidirect |
| 21. #14523976 | C22 | semidirect |
| 22. #14523976 | C22 | semidirect |
| 23. #14523976 | C22 | semidirect |
| 24. #14523974 | C22 | semidirect |
| 25. #14523974 | C22 | semidirect |
| 26. #14523974 | C22 | semidirect |
| 27. C4⋊(C67⋊C8) | C22 | semidirect |
| 28. C4⋊(C67⋊C8) | C22 | semidirect |
| 34. C4⋊Q8×C67 | C22 | semidirect |
| 36. #125×C67 | C22 | semidirect |
| 44. C2×D268 | Q8 | semidirect |
| 125. C67 | #3081 | semidirect |
| 126. #544 | D67 | semidirect |
| 141. C4⋊Q8 | C2×D67 | semidirect |
| 143. #125 | C2×D67 | semidirect |