Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14524090 | C2 | semidirect |
| 2. C22×#11761616 | C2 | semidirect |
| 3. #16863963 | C2 | semidirect |
| 4. #16863538 | C2 | semidirect |
| 5. #16863533 | C2 | semidirect |
| 6. #16863406 | C2 | semidirect |
| 7. #16863392 | C2 | semidirect |
| 8. #16863364 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C67 | C2 | semidirect |
| 15. C2×#11761627 | C22 | semidirect |
| 18. C2×Q8×D67 | C22 | semidirect |
| 27. #14523968 | C22 | semidirect |
| 28. #14523967 | C22 | semidirect |
| 29. #14523964 | C22 | semidirect |
| 30. (C2×D67)⋊C8 | C22 | semidirect |
| 48. C2×Dic134 | D4 | semidirect |
| 69. #41×C67 | D4 | semidirect |
| 146. C67 | #3010 | semidirect |
| 148. C2×AGL(1,ℤ/8) | D67 | semidirect |
| 191. #41 | C22⋊D67 | semidirect |