Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
488 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 123 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. #16863941 | C2 | semidirect |
| 2. C2×D4×Dic67 | C2 | semidirect |
| 3. #16863715 | C2 | semidirect |
| 4. #16863712 | C2 | semidirect |
| 5. #16863684 | C2 | semidirect |
| 6. #16863589 | C2 | semidirect |
| 7. #16863530 | C2 | semidirect |
| 8. #16863508 | C2 | semidirect |
| 9. #16863505 | C2 | semidirect |
| 10. #16863450 | C2 | semidirect |
| 11. #447×C67 | C2 | semidirect |
| 15. #14524042 | C22 | semidirect |
| 16. #14524039 | C22 | semidirect |
| 24. D4×Dic67 | C22 | semidirect |
| 25. #14524005 | C22 | semidirect |
| 30. #14523975 | C22 | semidirect |
| 31. #14523974 | C22 | semidirect |
| 32. Dic67⋊C8 | C22 | semidirect |
| 33. #14523965 | C22 | semidirect |
| 35. #14523964 | C22 | semidirect |
| 37. #14523953 | C22 | semidirect |
| 94. D4×C67 | #41 | semidirect |
| 150. C67 | #3109 | semidirect |
| 158. #447 | D67 | semidirect |
| 249. D4 | #11761627 | semidirect |