Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
484 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#14524063 | C2 | semidirect |
| 2. C2×#14524051 | C2 | semidirect |
| 3. #16863977 | C2 | semidirect |
| 4. #16863974 | C2 | semidirect |
| 5. #16863645 | C2 | semidirect |
| 6. #16863641 | C2 | semidirect |
| 7. #16863636 | C2 | semidirect |
| 8. #16863631 | C2 | semidirect |
| 9. C2×#14523976 | C2 | semidirect |
| 10. #16863398 | C2 | semidirect |
| 11. #417×C67 | C2 | semidirect |
| 63. C2×C67⋊C8 | D4 | semidirect |
| 153. C67 | #3061 | semidirect |
| 164. #417 | D67 | semidirect |