Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
206 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 72 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. C3×C8×A4 | C2 | semidirect |
| 3. C22×C3×M16 | C3 | semidirect |
| 4. A4×M16 | C3 | direct (N × H) |
| 14. C22×C3×C8 | C2×C3 | semidirect |
| 15. C8×A4 | C2×C3 | semidirect |
| 20. C22×M16 | C32 | semidirect |
| 35. C3×M16 | A4 | direct (N × H) |
| 39. C3×A4 | M16 | direct (N × H) |
| 46. C22×C8 | C2×C32 | semidirect |
| 66. C3×C8 | C2×A4 | semidirect |
| 79. M16 | C3×A4 | direct (N × H) |
| 90. C22×C3 | C3×M16 | semidirect |
| 92. A4 | C3×M16 | direct (N × H) |
| 115. C8 | C2×C3×A4 | semidirect |
| 130. C22 | C32×M16 | semidirect |
| 137. C3 | A4×M16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×A4 | 2 |
| C3×C8×A4 | 2 |
| C22×C3×M16 | 3 |
| A4×M16 | 3 |
| C32×M16 | 4 |