Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
482 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 131 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×Q16×D67 | C2 | semidirect |
| 2. #16864053 | C2 | semidirect |
| 3. #16863779 | C2 | semidirect |
| 4. #16863637 | C2 | semidirect |
| 5. #16863629 | C2 | semidirect |
| 6. #16863616 | C2 | semidirect |
| 7. #16863558 | C2 | semidirect |
| 8. #16863533 | C2 | semidirect |
| 9. Q16×Dic67 | C2 | semidirect |
| 10. C8×C22⋊D67 | C2 | semidirect |
| 11. C2×#135×C67 | C2 | semidirect |
| 74. Q16×C67 | D4 | semidirect |
| 120. C2×D67 | #135 | semidirect |
| 137. C67 | #3285 | semidirect |
| 138. C2×#135 | D67 | semidirect |
| 195. Q16 | C22⋊D67 | semidirect |