Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
174 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 59 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. D8×Dic67 | C2 | semidirect |
| 3. #16863478 | C2 | semidirect |
| 4. #16863221 | C2 | semidirect |
| 5. #16863198 | C2 | semidirect |
| 6. C16×Dic67 | C2 | semidirect |
| 7. #357×C67 | C2 | semidirect |
| 11. #14523984 | C4 | semidirect |
| 24. D536 | C2×C4 | semidirect |
| 30. C67⋊C16 | C2×C4 | semidirect |
| 33. D8×C67 | C2×C4 | semidirect |
| 65. Dic67 | D16 | semidirect |
| 72. C67 | C4×D16 | semidirect |
| 78. #357 | D67 | semidirect |
| 99. D8 | C4×D67 | semidirect |