Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
282 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 67 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. #16864027 | C2 | semidirect |
| 4. #16863157 | C2 | semidirect |
| 5. #343×C67 | C2 | semidirect |
| 22. C2×D268 | Q8 | semidirect |
| 82. C67 | #2027 | semidirect |
| 86. #343 | D67 | semidirect |