Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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×#14524031 | C2 | semidirect |
| 2. #16863778 | C2 | semidirect |
| 3. #16863753 | C2 | semidirect |
| 4. #16863618 | C2 | semidirect |
| 5. #16863611 | C2 | semidirect |
| 6. #16863551 | C2 | semidirect |
| 7. #16863546 | C2 | semidirect |
| 8. #16863534 | C2 | semidirect |
| 10. #16863449 | C2 | semidirect |
| 11. #529×C67 | C2 | semidirect |
| 14. C2×#11761618 | C22 | semidirect |
| 15. C2×#11761616 | C22 | semidirect |
| 24. C4⋊(C67⋊C8) | C22 | semidirect |
| 25. #14523966 | C22 | semidirect |
| 26. #14523966 | C22 | semidirect |
| 31. C4×C67⋊C8 | C22 | semidirect |
| 33. #125×C67 | C22 | semidirect |
| 34. #124×C67 | C22 | semidirect |
| 38. C4×Q8×C67 | C22 | semidirect |
| 40. C4×D4×C67 | C22 | semidirect |
| 144. C67 | #3211 | semidirect |
| 145. #529 | D67 | semidirect |
| 163. #125 | C2×D67 | semidirect |
| 168. #124 | C2×D67 | semidirect |
| 172. C4×Q8 | C2×D67 | semidirect |
| 174. C4×D4 | C2×D67 | semidirect |