Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
312 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 312 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. C2×#14523966 | C2 | semidirect |
| 5. C2×#14523961 | C2 | semidirect |
| 6. #16863160 | C2 | semidirect |
| 7. #343×C67 | C2 | semidirect |
| 11. #14524076 | C4 | semidirect |
| 117. C67 | #1908 | semidirect |
| 123. #343 | D67 | semidirect |