Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
514 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 115 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. C2×#14524014 | C2 | semidirect |
| 2. #121×D67 | C2 | semidirect |
| 3. #16863715 | C2 | semidirect |
| 4. #16863713 | C2 | semidirect |
| 5. #16863712 | C2 | semidirect |
| 6. #16863648 | C2 | semidirect |
| 7. #16863646 | C2 | semidirect |
| 8. #16863530 | C2 | semidirect |
| 9. #16863528 | C2 | semidirect |
| 10. #16863358 | C2 | semidirect |
| 11. #447×C67 | C2 | semidirect |
| 14. C2×D4×D67 | C22 | semidirect |
| 16. C2×#11761613 | C22 | semidirect |
| 17. C2×#11761611 | C22 | semidirect |
| 18. #14524018 | C22 | semidirect |
| 25. #14524014 | C22 | semidirect |
| 26. #14524014 | C22 | semidirect |
| 27. C2×C4⋊Dic67 | C22 | semidirect |
| 28. C4⋊C4×D67 | C22 | semidirect |
| 31. #14523975 | C22 | semidirect |
| 32. #14523974 | C22 | semidirect |
| 33. #14523965 | C22 | semidirect |
| 34. #14523964 | C22 | semidirect |
| 35. #14523964 | C22 | semidirect |
| 36. C22⋊(C67⋊C8) | C22 | semidirect |
| 37. (C2×D67)⋊C8 | C22 | semidirect |
| 38. C22×D4×C67 | C22 | semidirect |
| 39. C2×D8×C67 | C22 | semidirect |
| 41. #102×C67 | C22 | semidirect |
| 42. C22⋊C8×C67 | C22 | semidirect |
| 169. C67 | #3192 | semidirect |
| 179. #447 | D67 | semidirect |
| 184. C22×D4 | C2×D67 | semidirect |
| 187. C2×D8 | C2×D67 | semidirect |
| 208. #102 | C2×D67 | semidirect |
| 211. C22⋊C8 | C2×D67 | semidirect |