Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
156 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 69 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. #16863224 | C2 | semidirect |
| 5. #16863223 | C2 | semidirect |
| 6. #16863221 | C2 | semidirect |
| 7. #366×C67 | C2 | semidirect |
| 11. #14523982 | C4 | semidirect |
| 30. C67⋊C16 | C2×C4 | semidirect |
| 34. C16×C67 | C2×C4 | semidirect |
| 64. C67 | #2159 | semidirect |
| 71. #366 | D67 | semidirect |
| 98. C16 | C4×D67 | semidirect |