Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
494 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 139 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. D4×D268 | C2 | semidirect |
| 2. #16863744 | C2 | semidirect |
| 3. #16863709 | C2 | semidirect |
| 4. #16863673 | C2 | semidirect |
| 5. #16863630 | C2 | semidirect |
| 6. #16863591 | C2 | semidirect |
| 7. #16863529 | C2 | semidirect |
| 8. C4×#11761613 | C2 | semidirect |
| 9. D4×C67⋊C8 | C2 | semidirect |
| 10. C2×#14523963 | C2 | semidirect |
| 11. #547×C67 | C2 | semidirect |
| 15. C2×#11761613 | C22 | semidirect |
| 16. C22×C67⋊C8 | C22 | semidirect |
| 22. #14523976 | C22 | semidirect |
| 23. #14523976 | C22 | semidirect |
| 24. C4⋊(C67⋊C8) | C22 | semidirect |
| 25. #14523964 | C22 | semidirect |
| 28. #14523963 | C22 | semidirect |
| 29. #14523963 | C22 | semidirect |
| 30. #14523963 | C22 | semidirect |
| 31. C22⋊(C67⋊C8) | C22 | semidirect |
| 32. C4×C67⋊C8 | C22 | semidirect |
| 34. C4⋊Q8×C67 | C22 | semidirect |
| 37. #121×C67 | C22 | semidirect |
| 39. C4×D4×C67 | C22 | semidirect |
| 40. C2×C4⋊C4×C67 | C22 | semidirect |
| 89. D4×C67 | D8 | semidirect |
| 108. D268 | #41 | semidirect |
| 143. C67 | #3294 | semidirect |
| 144. #547 | D67 | semidirect |
| 161. C4⋊Q8 | C2×D67 | semidirect |
| 167. #121 | C2×D67 | semidirect |
| 171. C4×D4 | C2×D67 | semidirect |
| 172. C2×C4⋊C4 | C2×D67 | semidirect |
| 240. D4 | #11761613 | semidirect |