Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
327 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 327 conjugacy classes of subgroups — too many to draw. Only its 78 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. C3×#936 | C2 | semidirect |
| 3. C3×#909 | C2 | semidirect |
| 4. C32×#100 | C2 | semidirect |
| 5. C3×#825 | C2 | semidirect |
| 7. #4746 | C3 | direct (N × H) |
| 13. C2×C3×Dic6 | C22 | semidirect |
| 14. C32×M16 | C22 | semidirect |
| 16. C3×C4×Dic3 | C22 | semidirect |
| 23. #936 | C2×C3 | semidirect |
| 24. #909 | C2×C3 | semidirect |
| 27. C3×#100 | D3 | semidirect |
| 28. C3×#100 | C2×C3 | semidirect |
| 29. #825 | C2×C3 | semidirect |
| 57. C2×Dic6 | C22×C3 | semidirect |
| 61. C3×M16 | C2×D3 | semidirect |
| 62. C3×M16 | C22×C3 | semidirect |
| 66. C4×Dic3 | C22×C3 | semidirect |
| 82. #100 | C3×D3 | semidirect |
| 127. M16 | C2×C3×D3 | semidirect |
| 152. C32 | #455 | semidirect |
| 188. C3 | #4746 | direct (N × H) |
| 189. C3 | C3×#455 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#1004 | 2 |
| C3×#936 | 2 |
| C3×#909 | 2 |
| C32×#100 | 2 |
| C3×#825 | 2 |
| C3×#455 | 3 |
| #4746 | 3 |