Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
440 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 145 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. #16863683 | C2 | semidirect |
| 4. #16863673 | C2 | semidirect |
| 5. #16863439 | C2 | semidirect |
| 6. #16863420 | C2 | semidirect |
| 8. #533×C67 | C2 | semidirect |
| 18. #14523976 | C22 | semidirect |
| 19. #14523974 | C22 | semidirect |
| 20. C4⋊(C67⋊C8) | C22 | semidirect |
| 21. C4⋊(C67⋊C8) | C22 | semidirect |
| 24. C4⋊Q8×C67 | C22 | semidirect |
| 25. C4⋊Q8×C67 | C22 | semidirect |
| 26. #125×C67 | C22 | semidirect |
| 36. C2×D268 | Q8 | semidirect |
| 116. C67 | #3077 | semidirect |
| 117. #533 | D67 | semidirect |
| 128. C4⋊Q8 | C2×D67 | semidirect |
| 129. C4⋊Q8 | C2×D67 | semidirect |
| 130. #125 | C2×D67 | semidirect |