Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#14524032 | C2 | semidirect |
| 3. #41×Dic67 | C2 | semidirect |
| 4. #16863620 | C2 | semidirect |
| 5. #16863613 | C2 | semidirect |
| 6. #16863419 | C2 | semidirect |
| 7. #16863405 | C2 | semidirect |
| 8. #16863402 | C2 | semidirect |
| 9. C2×#137×C67 | C2 | semidirect |
| 18. Q8×Dic67 | C22 | semidirect |
| 20. D4×Dic67 | C22 | semidirect |
| 26. Dic67⋊C8 | C22 | semidirect |
| 27. #14523967 | C22 | semidirect |
| 32. C2×Q16×C67 | C22 | semidirect |
| 33. C2×SD16×C67 | C22 | semidirect |
| 126. C67 | #3040 | semidirect |
| 127. C2×#137 | D67 | semidirect |
| 141. C2×Q16 | C2×D67 | semidirect |
| 143. C2×SD16 | C2×D67 | semidirect |