Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
520 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 145 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. C22×C8×D67 | C2 | semidirect |
| 2. #16863903 | C2 | semidirect |
| 3. #16863634 | C2 | semidirect |
| 4. #16863629 | C2 | semidirect |
| 5. #16863622 | C2 | semidirect |
| 6. #16863434 | C2 | semidirect |
| 7. #16863392 | C2 | semidirect |
| 8. C2×#135×C67 | C2 | semidirect |
| 20. #14523977 | C22 | semidirect |
| 21. #14523975 | C22 | semidirect |
| 22. #14523967 | C22 | semidirect |
| 23. #14523964 | C22 | semidirect |
| 26. C2×Q16×C67 | C22 | semidirect |
| 27. C2×SD16×C67 | C22 | semidirect |
| 28. C2×D8×C67 | C22 | semidirect |
| 57. C2×C8×C67 | D4 | semidirect |
| 94. C2×D67 | #135 | semidirect |
| 107. C67 | #3050 | semidirect |
| 108. C2×#135 | D67 | semidirect |
| 119. C2×Q16 | C2×D67 | semidirect |
| 120. C2×SD16 | C2×D67 | semidirect |
| 121. C2×D8 | C2×D67 | semidirect |
| 158. C2×C8 | C22⋊D67 | semidirect |