Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
512 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 2. C2×C4⋊C4×D67 | C2 | semidirect |
| 3. #16863711 | C2 | semidirect |
| 4. #16863710 | C2 | semidirect |
| 5. #16863709 | C2 | semidirect |
| 6. #16863708 | C2 | semidirect |
| 7. #16863707 | C2 | semidirect |
| 8. #107×D67 | C2 | semidirect |
| 9. #102×D67 | C2 | semidirect |
| 10. C22⋊C8×D67 | C2 | semidirect |
| 11. #480×C67 | C2 | semidirect |
| 22. C2×C4⋊Dic67 | C22 | semidirect |
| 28. C4⋊C4×D67 | C22 | semidirect |
| 30. #14523977 | C22 | semidirect |
| 31. #14523976 | C22 | semidirect |
| 32. #14523976 | C22 | semidirect |
| 33. #14523965 | C22 | semidirect |
| 34. #14523964 | C22 | semidirect |
| 35. #14523963 | C22 | semidirect |
| 36. C22⋊(C67⋊C8) | C22 | semidirect |
| 37. (C2×D67)⋊C8 | C22 | semidirect |
| 39. C2×C4⋊C4×C67 | C22 | semidirect |
| 40. #107×C67 | C22 | semidirect |
| 41. #102×C67 | C22 | semidirect |
| 42. C22⋊C8×C67 | C22 | semidirect |
| 155. D67 | #480 | direct (N × H) |
| 157. C67 | C2×#480 | semidirect |
| 165. #480 | D67 | direct (N × H) |
| 187. C2×C4⋊C4 | C2×D67 | semidirect |
| 192. #107 | C2×D67 | semidirect |
| 196. #102 | C2×D67 | semidirect |
| 199. C22⋊C8 | C2×D67 | semidirect |