Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
302 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. #16863265 | C2 | semidirect |
| 5. #16863164 | C2 | semidirect |
| 6. #16863155 | C2 | semidirect |
| 7. #428×C67 | C2 | semidirect |
| 18. #14523969 | C4 | semidirect |
| 47. C4×Dic67 | C2×C4 | semidirect |
| 51. M16×C67 | C2×C4 | semidirect |
| 80. D268 | C4⋊C4 | semidirect |
| 85. Dic134 | C4⋊C4 | semidirect |
| 113. C67 | #1859 | semidirect |
| 115. #428 | D67 | semidirect |
| 155. M16 | C4×D67 | semidirect |