Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
230 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 56 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. C3×D4×A4 | C2 | semidirect |
| 2. C3×C8×A4 | C2 | semidirect |
| 3. C22×C3×D8 | C3 | semidirect |
| 4. A4×D8 | C3 | direct (N × H) |
| 8. C22×C3×D4 | C2×C3 | semidirect |
| 9. D4×A4 | C2×C3 | semidirect |
| 13. C22×C3×C8 | C2×C3 | semidirect |
| 14. C8×A4 | C2×C3 | semidirect |
| 19. C22×D8 | C32 | semidirect |
| 31. C3×D8 | A4 | direct (N × H) |
| 35. C3×A4 | D8 | direct (N × H) |
| 37. C22×D4 | C2×C32 | semidirect |
| 41. C22×C8 | C2×C32 | semidirect |
| 53. C3×D4 | C2×A4 | semidirect |
| 58. C3×C8 | C2×A4 | semidirect |
| 69. D8 | C3×A4 | direct (N × H) |
| 81. C22×C3 | C3×D8 | semidirect |
| 82. A4 | C3×D8 | direct (N × H) |
| 95. D4 | C2×C3×A4 | semidirect |
| 99. C8 | C2×C3×A4 | semidirect |
| 115. C22 | C32×D8 | semidirect |
| 119. C3 | A4×D8 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D4×A4 | 2 |
| C3×C8×A4 | 2 |
| C22×C3×D8 | 3 |
| A4×D8 | 3 |
| C32×D8 | 4 |