Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×C8×D67 | C2 | semidirect |
| 2. C2×#14524019 | C2 | semidirect |
| 4. #16863622 | C2 | direct (N × H) |
| 5. C2×#14523975 | C2 | semidirect |
| 6. C2×#14523967 | C2 | semidirect |
| 7. C2×#14523964 | C2 | semidirect |
| 8. C22×SD16×C67 | C2 | semidirect |
| 13. C2×C8×D67 | C22 | semidirect |
| 15. #14524019 | C22 | semidirect |
| 23. #14523975 | C22 | semidirect |
| 24. #14523967 | C22 | semidirect |
| 25. #14523964 | C22 | semidirect |
| 29. C2×SD16×C67 | C22 | semidirect |
| 63. C2×C8×C67 | D4 | semidirect |
| 72. C22×D67 | SD16 | semidirect |
| 96. C8×C67 | C2×D4 | semidirect |
| 109. C2×D67 | C2×SD16 | semidirect |
| 118. C2×C67 | #465 | semidirect |
| 124. C67 | C2×#465 | semidirect |
| 125. C22×SD16 | D67 | semidirect |
| 138. C2×SD16 | C2×D67 | semidirect |
| 180. C2×C8 | C22⋊D67 | semidirect |
| 221. C8 | C2×C22⋊D67 | semidirect |
| 243. C2 | #16863622 | direct (N × H) |