Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
758 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 758 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11761627 | C2 | semidirect |
| 2. C2×#14524073 | C2 | semidirect |
| 3. #16863903 | C2 | semidirect |
| 4. #16863555 | C2 | semidirect |
| 5. #16863538 | C2 | semidirect |
| 6. #16863406 | C2 | semidirect |
| 7. #16863401 | C2 | semidirect |
| 8. #16863359 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C67 | C2 | semidirect |
| 19. C2×#11761618 | C22 | semidirect |
| 20. C2×#11761616 | C22 | semidirect |
| 23. #14524019 | C22 | semidirect |
| 24. #14524014 | C22 | semidirect |
| 28. #14523968 | C22 | semidirect |
| 29. #14523964 | C22 | semidirect |
| 30. (C2×D67)⋊C8 | C22 | semidirect |
| 34. C2×SD16×C67 | C22 | semidirect |
| 35. C2×D8×C67 | C22 | semidirect |
| 43. C2×Dic134 | D4 | semidirect |
| 73. C2×D4×C67 | D4 | semidirect |
| 146. C67 | #3005 | semidirect |
| 149. C2×AGL(1,ℤ/8) | D67 | semidirect |
| 170. C2×SD16 | C2×D67 | semidirect |
| 171. C2×D8 | C2×D67 | semidirect |
| 201. C2×D4 | C22⋊D67 | semidirect |