Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
388 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 3. C2×#14523953 | C2 | semidirect |
| 4. C4⋊C4×Dic67 | C2 | semidirect |
| 5. #16863159 | C2 | semidirect |
| 6. #16863158 | C2 | semidirect |
| 11. D4×Dic67 | C4 | semidirect |
| 17. #14523964 | C4 | semidirect |
| 23. #102×C67 | C4 | semidirect |
| 33. C2×C67⋊C8 | C2×C4 | semidirect |
| 37. C4⋊Dic67 | C2×C4 | semidirect |
| 53. C2×C8×C67 | C2×C4 | semidirect |
| 55. C4⋊C4×C67 | C2×C4 | semidirect |
| 67. D4×C67 | C42 | semidirect |
| 124. C67 | #1762 | semidirect |
| 145. #102 | Dic67 | semidirect |
| 169. C2×C8 | C2×Dic67 | semidirect |
| 175. C4⋊C4 | C2×Dic67 | semidirect |
| 191. D4 | C4×Dic67 | semidirect |