Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
466 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 113 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. #16863906 | C2 | semidirect |
| 2. C2×#14524018 | C2 | semidirect |
| 3. #16863726 | C2 | semidirect |
| 4. #16863723 | C2 | semidirect |
| 5. #16863648 | C2 | semidirect |
| 6. #16863643 | C2 | semidirect |
| 7. #16863549 | C2 | semidirect |
| 8. #16863542 | C2 | semidirect |
| 9. #16863529 | C2 | semidirect |
| 10. #16863358 | C2 | semidirect |
| 11. #480×C67 | C2 | semidirect |
| 12. C2×#11761627 | C22 | semidirect |
| 16. C2×#11761617 | C22 | semidirect |
| 17. C2×#11761613 | C22 | semidirect |
| 18. C2×#11761611 | C22 | semidirect |
| 20. #14524023 | C22 | semidirect |
| 26. #14524014 | C22 | semidirect |
| 30. #14524001 | C22 | semidirect |
| 32. #14523974 | C22 | semidirect |
| 33. #14523966 | C22 | semidirect |
| 34. #14523965 | C22 | semidirect |
| 35. #14523963 | C22 | semidirect |
| 37. (C2×D67)⋊C8 | C22 | semidirect |
| 40. #107×C67 | C22 | semidirect |
| 41. #102×C67 | C22 | semidirect |
| 159. C67 | #3194 | semidirect |
| 164. #480 | D67 | semidirect |
| 193. #107 | C2×D67 | semidirect |
| 198. #102 | C2×D67 | semidirect |