Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 121 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. #16863788 | C2 | semidirect |
| 3. #16863758 | C2 | semidirect |
| 4. #16863618 | C2 | semidirect |
| 5. #16863551 | C2 | semidirect |
| 7. #16863453 | C2 | semidirect |
| 8. #533×C67 | C2 | semidirect |
| 11. C2×#11761618 | C22 | semidirect |
| 19. C4⋊(C67⋊C8) | C22 | semidirect |
| 20. #14523966 | C22 | semidirect |
| 23. #14523954 | C22 | semidirect |
| 24. C4⋊Q8×C67 | C22 | semidirect |
| 25. C4⋊Q8×C67 | C22 | semidirect |
| 30. C4×Q8×C67 | C22 | semidirect |
| 113. C67 | #3215 | semidirect |
| 114. #533 | D67 | semidirect |
| 126. C4⋊Q8 | C2×D67 | semidirect |
| 127. C4⋊Q8 | C2×D67 | semidirect |
| 136. C4×Q8 | C2×D67 | semidirect |