Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
482 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 125 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×#14524062 | C2 | semidirect |
| 2. C22×Dic268 | C2 | semidirect |
| 3. #16864052 | C2 | semidirect |
| 4. #16863779 | C2 | semidirect |
| 5. #16863638 | C2 | semidirect |
| 6. #16863617 | C2 | semidirect |
| 7. #16863559 | C2 | semidirect |
| 8. #16863534 | C2 | semidirect |
| 9. #16863490 | C2 | semidirect |
| 10. C8×C22⋊D67 | C2 | semidirect |
| 11. #466×C67 | C2 | semidirect |
| 55. Dic268 | D4 | semidirect |
| 116. C22×C67 | #135 | semidirect |
| 137. C67 | #3285 | semidirect |
| 143. #466 | D67 | semidirect |
| 256. C22 | #14524062 | semidirect |