Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
584 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×Q8×Dic67 | C2 | semidirect |
| 4. #16863594 | C2 | direct (N × H) |
| 5. C2×Dic67⋊C8 | C2 | semidirect |
| 6. C2×#14523965 | C2 | semidirect |
| 7. C2×#14523964 | C2 | semidirect |
| 8. C22×SD16×C67 | C2 | semidirect |
| 13. C2×#11761615 | C22 | semidirect |
| 18. Q8×Dic67 | C22 | semidirect |
| 23. Dic67⋊C8 | C22 | semidirect |
| 24. #14523965 | C22 | semidirect |
| 25. #14523964 | C22 | semidirect |
| 29. C2×SD16×C67 | C22 | semidirect |
| 55. C2×Q8×C67 | D4 | semidirect |
| 77. Q8×C67 | C2×D4 | semidirect |
| 92. C2×Dic67 | SD16 | semidirect |
| 118. Dic67 | C2×SD16 | semidirect |
| 120. C2×C67 | #460 | semidirect |
| 126. C67 | C2×#460 | semidirect |
| 128. C22×SD16 | D67 | semidirect |
| 143. C2×SD16 | C2×D67 | semidirect |
| 161. C2×Q8 | C22⋊D67 | semidirect |
| 203. Q8 | C2×C22⋊D67 | semidirect |
| 247. C2 | #16863594 | direct (N × H) |