Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
342 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 3. #16863794 | C2 | semidirect |
| 4. #16863735 | C2 | semidirect |
| 5. #16863725 | C2 | semidirect |
| 6. #16863691 | C2 | semidirect |
| 7. #16863681 | C2 | semidirect |
| 8. #16863651 | C2 | semidirect |
| 10. #16863437 | C2 | semidirect |
| 11. C4×Q16×C67 | C2 | semidirect |
| 117. C67 | #3356 | semidirect |
| 126. C4×Q16 | D67 | semidirect |