Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 3. #16863222 | C2 | semidirect |
| 4. #16863200 | C2 | semidirect |
| 5. C2×Q32×C67 | C2 | semidirect |
| 43. C2×D67 | Q32 | semidirect |
| 54. C67 | #2216 | semidirect |
| 55. C2×Q32 | D67 | semidirect |