Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
264 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. C2×#14523978 | C2 | semidirect |
| 3. C2×#14523976 | C2 | semidirect |
| 6. #16863164 | C2 | semidirect |
| 7. #343×C67 | C2 | semidirect |
| 10. #14524051 | C4 | semidirect |
| 104. C67 | #1816 | semidirect |
| 111. #343 | D67 | semidirect |