Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 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. C2×#14524073 | C2 | semidirect |
| 3. C2×#14524031 | C2 | semidirect |
| 4. #16863618 | C2 | semidirect |
| 5. #16863611 | C2 | semidirect |
| 6. #16863420 | C2 | semidirect |
| 7. #16863404 | C2 | semidirect |
| 8. #16863400 | C2 | semidirect |
| 9. C4×#41×C67 | C2 | semidirect |
| 14. C2×#11761618 | C22 | semidirect |
| 15. C2×#11761616 | C22 | semidirect |
| 24. C4⋊(C67⋊C8) | C22 | semidirect |
| 25. #14523966 | C22 | semidirect |
| 28. C4×Q8×C67 | C22 | semidirect |
| 30. C4×D4×C67 | C22 | semidirect |
| 126. C67 | #3040 | semidirect |
| 130. C4×#41 | D67 | semidirect |
| 150. C4×Q8 | C2×D67 | semidirect |
| 152. C4×D4 | C2×D67 | semidirect |