Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
422 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 75 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×Q8×A4 | C2 | semidirect |
| 3. A4×Dic6 | C2 | semidirect |
| 4. C22×D3×Q8 | C3 | semidirect |
| 10. C22×C3×Q8 | C2×C3 | semidirect |
| 16. C22×Dic6 | C2×C3 | semidirect |
| 19. Q8×A4 | D3 | direct (N × H) |
| 22. D3×A4 | Q8 | direct (N × H) |
| 40. D3×Q8 | A4 | direct (N × H) |
| 52. C3×A4 | C2×Q8 | semidirect |
| 60. C22×Q8 | C3×D3 | semidirect |
| 66. C22×D3 | C3×Q8 | semidirect |
| 75. C3×Q8 | C2×A4 | semidirect |
| 89. Dic6 | C2×A4 | semidirect |
| 114. C22×C3 | C2×C3×Q8 | semidirect |
| 122. A4 | D3×Q8 | direct (N × H) |
| 142. Q8 | D3×A4 | direct (N × H) |
| 159. D3 | Q8×A4 | direct (N × H) |
| 168. C22 | C3×D3×Q8 | semidirect |
| 175. C3 | C2×Q8×A4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×A4 | 2 |
| C4×D3×A4 | 2 |
| A4×Dic6 | 2 |
| C22×D3×Q8 | 3 |
| C2×Q8×A4 | 3 |
| C3×D3×Q8 | 4 |