Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14524076 | C2 | semidirect |
| 3. #16863967 | C2 | semidirect |
| 4. #16863654 | C2 | semidirect |
| 5. #16863642 | C2 | semidirect |
| 6. #16863637 | C2 | semidirect |
| 7. #16863625 | C2 | semidirect |
| 8. #16863438 | C2 | semidirect |
| 9. #16863393 | C2 | semidirect |
| 10. C2×#14523968 | C2 | semidirect |
| 11. C2×#131×C67 | C2 | semidirect |
| 79. M16×C67 | D4 | semidirect |
| 144. C67 | #3063 | semidirect |
| 146. C2×#131 | D67 | semidirect |
| 210. M16 | C22⋊D67 | semidirect |