Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 490 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 |
|---|---|---|
| 1. C22×#11761615 | C2 | semidirect |
| 3. #16863874 | C2 | semidirect |
| 4. #16863620 | C2 | semidirect |
| 5. #16863594 | C2 | semidirect |
| 6. #16863424 | C2 | semidirect |
| 7. #16863402 | C2 | semidirect |
| 8. #16863392 | C2 | semidirect |
| 9. C2×#137×C67 | C2 | semidirect |
| 19. Q8×Dic67 | C22 | semidirect |
| 23. Dic67⋊C8 | C22 | semidirect |
| 24. #14523967 | C22 | semidirect |
| 26. #14523964 | C22 | semidirect |
| 30. C2×Q16×C67 | C22 | semidirect |
| 31. C2×SD16×C67 | C22 | semidirect |
| 55. C2×Q8×C67 | D4 | semidirect |
| 117. C67 | #3043 | semidirect |
| 118. C2×#137 | D67 | semidirect |
| 131. C2×Q16 | C2×D67 | semidirect |
| 134. C2×SD16 | C2×D67 | semidirect |
| 155. C2×Q8 | C22⋊D67 | semidirect |