Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
174 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 33 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. A4×Dic6 | C2 | semidirect |
| 3. C3×C8×A4 | C2 | semidirect |
| 4. C22×#204 | C3 | semidirect |
| 11. C22×Dic6 | C2×C3 | semidirect |
| 14. C22×C3×C8 | C2×C3 | semidirect |
| 20. C8×A4 | D3 | semidirect |
| 47. #204 | A4 | direct (N × H) |
| 49. C3×A4 | SD16 | semidirect |
| 58. C22×C8 | C3×D3 | semidirect |
| 80. Dic6 | C2×A4 | semidirect |
| 84. C3×C8 | C2×A4 | semidirect |
| 106. C22×C3 | C3×SD16 | semidirect |
| 114. A4 | #204 | direct (N × H) |
| 141. C8 | D3×A4 | semidirect |
| 158. C22 | C3×#204 | semidirect |
| 165. C3 | A4×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×D12 | 2 |
| A4×Dic6 | 2 |
| C3×C8×A4 | 2 |
| C22×#204 | 3 |
| A4×SD16 | 3 |
| C3×#204 | 4 |