Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
414 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 126 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. C2×C32×M16 | C2 | semidirect |
| 3. C3×#926 | C2 | semidirect |
| 4. C3×#821 | C2 | semidirect |
| 6. #5131 | C3 | direct (N × H) |
| 11. C2×C3×D12 | C4 | semidirect |
| 14. C2×C32×C8 | C22 | semidirect |
| 16. C3×C4⋊Dic3 | C22 | semidirect |
| 21. C2×C3×M16 | D3 | semidirect |
| 22. C2×C3×M16 | C2×C3 | semidirect |
| 24. #926 | C2×C3 | semidirect |
| 26. #821 | C2×C3 | semidirect |
| 52. C2×D12 | C3×C4 | semidirect |
| 58. C2×C3×C8 | C2×D3 | semidirect |
| 59. C2×C3×C8 | C22×C3 | semidirect |
| 64. C4⋊Dic3 | C22×C3 | semidirect |
| 77. C2×M16 | C3×D3 | semidirect |
| 123. C2×C8 | C2×C3×D3 | semidirect |
| 153. C32 | #418 | semidirect |
| 189. C3 | #5131 | direct (N × H) |
| 190. C3 | C3×#418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D12 | 2 |
| C2×C32×M16 | 2 |
| C3×#926 | 2 |
| C3×#821 | 2 |
| C3×#418 | 3 |
| #5131 | 3 |