Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
548 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 548 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. C2×#14524068 | C2 | semidirect |
| 2. C2×C4×D268 | C2 | semidirect |
| 3. #16863608 | C2 | semidirect |
| 4. #16863598 | C2 | semidirect |
| 5. #16863588 | C2 | semidirect |
| 6. #16863420 | C2 | semidirect |
| 7. #16863397 | C2 | semidirect |
| 8. #532×C67 | C2 | semidirect |
| 21. C4⋊(C67⋊C8) | C22 | semidirect |
| 22. C4⋊(C67⋊C8) | C22 | semidirect |
| 23. #14523967 | C22 | semidirect |
| 24. #14523964 | C22 | semidirect |
| 26. C4⋊Q8×C67 | C22 | semidirect |
| 27. #127×C67 | C22 | semidirect |
| 28. #124×C67 | C22 | semidirect |
| 37. C2×D268 | D4 | semidirect |
| 119. C4×C67 | AGL(1,ℤ/8) | semidirect |
| 130. C67 | #3036 | semidirect |
| 132. #532 | D67 | semidirect |
| 146. C4⋊Q8 | C2×D67 | semidirect |
| 147. #127 | C2×D67 | semidirect |
| 148. #124 | C2×D67 | semidirect |
| 250. C4 | #14524068 | semidirect |