Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
300 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 3. #16863354 | C2 | semidirect |
| 4. C2×C4×C67⋊C8 | C2 | semidirect |
| 5. #16863160 | C2 | semidirect |
| 6. #16863156 | C2 | semidirect |
| 9. #14524050 | C4 | semidirect |
| 16. #14523967 | C4 | semidirect |
| 17. #14523964 | C4 | semidirect |
| 24. #104×C67 | C4 | semidirect |
| 99. C67 | #1764 | semidirect |
| 118. #104 | Dic67 | semidirect |