Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
254 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 5. #4555 | C3 | direct (N × H) |
| 9. C32×M16 | C4 | semidirect |
| 12. C3×C4⋊Dic3 | C4 | semidirect |
| 15. C3×C4×Dic3 | C4 | semidirect |
| 44. C3×M16 | Dic3 | semidirect |
| 45. C3×M16 | C3×C4 | semidirect |
| 55. C4⋊Dic3 | C3×C4 | semidirect |
| 58. C4×Dic3 | C3×C4 | semidirect |
| 109. M16 | C3×Dic3 | semidirect |
| 144. C32 | #339 | semidirect |
| 179. C3 | #4555 | direct (N × H) |
| 180. C3 | C3×#339 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×M16 | 2 |
| C3×#926 | 2 |
| C2×C3×C4×Dic3 | 2 |
| C3×#339 | 3 |
| #4555 | 3 |