Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 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×Q16×D67 | C2 | semidirect |
| 3. #16863774 | C2 | semidirect |
| 4. #16863637 | C2 | semidirect |
| 5. #16863634 | C2 | semidirect |
| 6. #16863604 | C2 | semidirect |
| 7. #16863552 | C2 | semidirect |
| 8. #16863550 | C2 | semidirect |
| 9. Q16×Dic67 | C2 | semidirect |
| 11. C22×Q16×C67 | C2 | semidirect |
| 76. Q16×C67 | D4 | semidirect |
| 94. C22⋊D67 | Q16 | direct (N × H) |
| 112. C22×C67 | C2×Q16 | semidirect |
| 116. C2×D67 | C2×Q16 | semidirect |
| 126. Dic67 | C2×Q16 | semidirect |
| 133. C67 | D4×Q16 | semidirect |
| 135. C22×Q16 | D67 | semidirect |
| 193. Q16 | C22⋊D67 | direct (N × H) |
| 248. C22 | Q16×D67 | semidirect |