Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
178 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 178 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 |
|---|---|---|
| 1. C3×Q8×A4 | C2 | semidirect |
| 3. A4×C3⋊C8 | C2 | semidirect |
| 4. C22×#215 | C3 | semidirect |
| 10. C22×C3×Q8 | C2×C3 | semidirect |
| 13. Q8×A4 | D3 | semidirect |
| 19. C22×C3⋊C8 | C2×C3 | semidirect |
| 46. #215 | A4 | direct (N × H) |
| 50. C3×A4 | SD16 | semidirect |
| 53. C22×Q8 | C3×D3 | semidirect |
| 73. C3×Q8 | C2×A4 | semidirect |
| 85. C3⋊C8 | C2×A4 | semidirect |
| 107. C22×C3 | C3×SD16 | semidirect |
| 115. A4 | #215 | direct (N × H) |
| 133. Q8 | D3×A4 | semidirect |
| 160. C22 | C3×#215 | semidirect |
| 167. C3 | A4×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×A4 | 2 |
| A4×D12 | 2 |
| A4×C3⋊C8 | 2 |
| C22×#215 | 3 |
| A4×SD16 | 3 |
| C3×#215 | 4 |