Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
484 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 143 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×#14524074 | C2 | semidirect |
| 3. C2×Q8×Dic67 | C2 | semidirect |
| 4. #16863620 | C2 | semidirect |
| 5. #16863616 | C2 | semidirect |
| 6. #16863604 | C2 | semidirect |
| 7. #16863594 | C2 | semidirect |
| 8. #16863419 | C2 | semidirect |
| 9. #16863398 | C2 | semidirect |
| 10. #16863397 | C2 | semidirect |
| 11. C2×#137×C67 | C2 | semidirect |
| 80. C2×Q8×C67 | D4 | semidirect |
| 150. Dic67 | #137 | semidirect |
| 158. C67 | #3037 | semidirect |
| 160. C2×#137 | D67 | semidirect |
| 210. C2×Q8 | C22⋊D67 | semidirect |