Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 125 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. #16864024 | C2 | semidirect |
| 3. #16863763 | C2 | semidirect |
| 4. #16863757 | C2 | semidirect |
| 5. #16863752 | C2 | semidirect |
| 6. #16863745 | C2 | semidirect |
| 9. C2×#14523967 | C2 | semidirect |
| 10. #16863354 | C2 | semidirect |
| 11. #419×C67 | C2 | semidirect |
| 128. C67 | #3137 | semidirect |
| 135. #419 | D67 | semidirect |