Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 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. C2×#14524074 | C2 | semidirect |
| 3. C4×#11761628 | C2 | semidirect |
| 4. #16863615 | C2 | semidirect |
| 5. #16863608 | C2 | semidirect |
| 6. #16863420 | C2 | semidirect |
| 7. #16863405 | C2 | semidirect |
| 8. #16863401 | C2 | semidirect |
| 9. C2×#124×C67 | C2 | semidirect |
| 13. C2×#11761618 | C22 | semidirect |
| 15. C2×#11761615 | C22 | semidirect |
| 19. C4×Dic134 | C22 | semidirect |
| 20. C4×D268 | C22 | semidirect |
| 25. C4⋊(C67⋊C8) | C22 | semidirect |
| 26. #14523967 | C22 | semidirect |
| 126. C67 | #3040 | semidirect |
| 129. C2×#124 | D67 | semidirect |