Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 141 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×#11761613 | C2 | semidirect |
| 2. C2×#14524050 | C2 | semidirect |
| 3. #16863960 | C2 | semidirect |
| 4. #16863647 | C2 | semidirect |
| 5. #16863630 | C2 | semidirect |
| 6. #16863432 | C2 | semidirect |
| 7. #16863401 | C2 | semidirect |
| 8. #16863400 | C2 | semidirect |
| 9. #535×C67 | C2 | semidirect |
| 16. C2×#11761612 | C22 | semidirect |
| 18. C22×C67⋊C8 | C22 | semidirect |
| 21. #14524017 | C22 | semidirect |
| 24. #14523976 | C22 | semidirect |
| 25. #14523974 | C22 | semidirect |
| 26. #14523964 | C22 | semidirect |
| 27. #14523963 | C22 | semidirect |
| 32. #121×C67 | C22 | semidirect |
| 46. C2×C67⋊C8 | D4 | semidirect |
| 126. C67 | #3058 | semidirect |
| 130. #535 | D67 | semidirect |
| 152. #121 | C2×D67 | semidirect |