Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
460 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 117 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. #16864111 | C2 | semidirect |
| 2. D4×D268 | C2 | semidirect |
| 3. #16863743 | C2 | semidirect |
| 4. #16863723 | C2 | semidirect |
| 5. #16863686 | C2 | semidirect |
| 6. #16863648 | C2 | semidirect |
| 7. #16863591 | C2 | semidirect |
| 8. #16863528 | C2 | semidirect |
| 9. #16863475 | C2 | semidirect |
| 10. #16863399 | C2 | semidirect |
| 11. C4×D8×C67 | C2 | semidirect |
| 14. C2×#11761613 | C22 | semidirect |
| 15. C2×#11761611 | C22 | semidirect |
| 16. #14524043 | C22 | semidirect |
| 22. #14524014 | C22 | semidirect |
| 26. #14524001 | C22 | semidirect |
| 27. #14523974 | C22 | semidirect |
| 28. C4⋊(C67⋊C8) | C22 | semidirect |
| 29. #14523965 | C22 | semidirect |
| 30. #14523965 | C22 | semidirect |
| 32. #14523963 | C22 | semidirect |
| 33. (C2×D67)⋊C8 | C22 | semidirect |
| 36. C4×D4×C67 | C22 | semidirect |
| 37. #107×C67 | C22 | semidirect |
| 39. #102×C67 | C22 | semidirect |
| 40. C4×C8×C67 | C22 | semidirect |
| 141. C67 | #3325 | semidirect |
| 150. C4×D8 | D67 | semidirect |
| 168. C4×D4 | C2×D67 | semidirect |
| 171. #107 | C2×D67 | semidirect |
| 179. #102 | C2×D67 | semidirect |
| 181. C4×C8 | C2×D67 | semidirect |