Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 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×#11761615 | C2 | semidirect |
| 2. C2×#14524050 | C2 | semidirect |
| 4. #16863644 | C2 | semidirect |
| 5. #16863627 | C2 | semidirect |
| 6. #16863432 | C2 | semidirect |
| 7. #16863405 | C2 | semidirect |
| 8. #16863400 | C2 | semidirect |
| 9. #536×C67 | C2 | semidirect |
| 16. C2×#11761612 | C22 | semidirect |
| 18. C22×C67⋊C8 | C22 | semidirect |
| 24. #14523976 | C22 | semidirect |
| 25. #14523974 | C22 | semidirect |
| 26. #14523967 | C22 | semidirect |
| 33. C22⋊Q8×C67 | C22 | semidirect |
| 46. C2×C67⋊C8 | D4 | semidirect |
| 121. C67 | #3057 | semidirect |
| 124. #536 | D67 | semidirect |
| 147. C22⋊Q8 | C2×D67 | semidirect |