Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 125 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. #16864106 | C2 | semidirect |
| 3. #16863743 | C2 | semidirect |
| 4. #16863716 | C2 | semidirect |
| 5. #16863686 | C2 | semidirect |
| 6. #16863628 | C2 | semidirect |
| 7. #16863596 | C2 | semidirect |
| 8. #16863545 | C2 | semidirect |
| 9. C8×D268 | C2 | semidirect |
| 10. #102×D67 | C2 | semidirect |
| 11. C4×SD16×C67 | C2 | semidirect |
| 14. C2×#11761615 | C22 | semidirect |
| 15. C2×C8×D67 | C22 | semidirect |
| 16. #14524043 | C22 | semidirect |
| 20. #14524019 | C22 | semidirect |
| 26. C4⋊C4×D67 | 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 |
| 35. C4×Q8×C67 | C22 | semidirect |
| 37. #106×C67 | C22 | semidirect |
| 38. #103×C67 | C22 | semidirect |
| 40. C4×C8×C67 | C22 | semidirect |
| 102. D268 | SD16 | semidirect |
| 137. C67 | #3295 | semidirect |
| 146. C4×SD16 | D67 | semidirect |
| 162. C4×Q8 | C2×D67 | semidirect |
| 168. #106 | C2×D67 | semidirect |
| 170. #103 | C2×D67 | semidirect |
| 177. C4×C8 | C2×D67 | semidirect |