Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
312 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 312 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. #64160 | C2 | semidirect |
| 3. #64157 | C2 | semidirect |
| 4. C2×#3754 | C2 | semidirect |
| 5. #63660 | C2 | semidirect |
| 6. #63651 | C2 | semidirect |
| 7. #63649 | C2 | semidirect |
| 121. C32 | #471 | semidirect |
| 150. C3 | #5200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×AGL(1,ℤ/8) | 2 |
| #64160 | 2 |
| #64157 | 2 |
| C2×#3754 | 2 |
| #63660 | 2 |
| #63651 | 2 |
| #63649 | 2 |
| #5200 | 3 |