Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
370 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 129 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. #16864201 | C2 | semidirect |
| 2. #16863834 | C2 | semidirect |
| 3. #16863828 | C2 | semidirect |
| 4. C2×D1072 | C2 | semidirect |
| 5. #504×C67 | C2 | semidirect |
| 8. #14524065 | C22 | semidirect |
| 9. C2×D536 | C22 | semidirect |
| 10. Dic536 | C22 | semidirect |
| 11. #14523988 | C22 | semidirect |
| 12. D1072 | C22 | semidirect |
| 13. D1072 | C22 | semidirect |
| 15. M32×C67 | C22 | semidirect |
| 16. C2×C16×C67 | C22 | semidirect |
| 51. C67 | #3415 | semidirect |
| 56. #504 | D67 | semidirect |
| 66. M32 | C2×D67 | semidirect |
| 67. C2×C16 | C2×D67 | semidirect |