Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
270 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 83 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. #64113 | C2 | semidirect |
| 2. C2×#3745 | C2 | semidirect |
| 3. C32×M32 | C2 | semidirect |
| 4. #63627 | C2 | semidirect |
| 5. #63626 | C2 | semidirect |
| 10. #3746 | C22 | semidirect |
| 13. #3745 | C22 | semidirect |
| 15. C32×C16 | C22 | semidirect |
| 18. C3×M32 | D3 | semidirect |
| 40. C3×C16 | C2×D3 | semidirect |
| 52. M32 | C3⋊D3 | semidirect |
| 75. C16 | C2×C3⋊D3 | semidirect |
| 83. C32 | #509 | semidirect |
| 105. C3 | #4908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64113 | 2 |
| C2×#3745 | 2 |
| C32×M32 | 2 |
| #63627 | 2 |
| #63626 | 2 |
| #4908 | 3 |