Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 157 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. C22×#11761612 | C2 | semidirect |
| 4. #16863644 | C2 | direct (N × H) |
| 5. C2×#14523976 | C2 | semidirect |
| 6. C2×#14523967 | C2 | semidirect |
| 7. C2×#14523963 | C2 | semidirect |
| 8. C2×C22⋊Q8×C67 | C2 | semidirect |
| 12. C2×#11761615 | C22 | semidirect |
| 14. C2×#11761612 | C22 | semidirect |
| 21. #14523976 | C22 | semidirect |
| 22. #14523967 | C22 | semidirect |
| 23. #14523963 | C22 | semidirect |
| 27. C22⋊Q8×C67 | C22 | semidirect |
| 42. C2×C67⋊C8 | D4 | semidirect |
| 97. C67⋊C8 | C2×D4 | semidirect |
| 118. C2×C67 | #468 | semidirect |
| 124. C67 | C2×#468 | semidirect |
| 127. C2×C22⋊Q8 | D67 | semidirect |
| 144. C22⋊Q8 | C2×D67 | semidirect |
| 243. C2 | #16863644 | direct (N × H) |