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×#14524073 | C2 | semidirect |
| 2. C2×#14524030 | C2 | semidirect |
| 3. #41×Dic67 | C2 | semidirect |
| 4. #16863616 | C2 | semidirect |
| 5. #16863609 | C2 | semidirect |
| 6. #16863419 | C2 | semidirect |
| 7. #16863406 | C2 | semidirect |
| 8. #16863401 | C2 | semidirect |
| 12. C2×#11761618 | C22 | semidirect |
| 13. C2×#11761616 | C22 | semidirect |
| 18. Q8×Dic67 | C22 | semidirect |
| 20. D4×Dic67 | C22 | semidirect |
| 26. Dic67⋊C8 | C22 | semidirect |
| 27. #14523968 | C22 | semidirect |
| 126. C67 | #3040 | semidirect |