Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
414 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 2. C2×#14524019 | C2 | semidirect |
| 3. #16863736 | C2 | semidirect |
| 4. #16863732 | C2 | semidirect |
| 5. #16863712 | C2 | semidirect |
| 6. #16863653 | C2 | semidirect |
| 7. #16863639 | C2 | semidirect |
| 8. #16863555 | C2 | semidirect |
| 9. #16863552 | C2 | semidirect |
| 10. #16863358 | C2 | semidirect |
| 11. #448×C67 | C2 | semidirect |
| 14. C2×#11761618 | C22 | semidirect |
| 31. #14523977 | C22 | semidirect |
| 32. #14523974 | C22 | semidirect |
| 33. #14523968 | C22 | semidirect |
| 34. #14523967 | C22 | semidirect |
| 35. #14523964 | C22 | semidirect |
| 39. C2×SD16×C67 | C22 | semidirect |
| 41. #103×C67 | C22 | semidirect |
| 150. C67 | #3196 | semidirect |
| 160. #448 | D67 | semidirect |
| 166. C2×SD16 | C2×D67 | semidirect |
| 188. #103 | C2×D67 | semidirect |