Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
238 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 82 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. C2×C3×Dic12 | C2 | semidirect |
| 4. C32×#106 | C2 | semidirect |
| 5. C3×#810 | C2 | semidirect |
| 7. #4867 | C3 | direct (N × H) |
| 20. C2×Dic12 | C2×C3 | semidirect |
| 24. C3×#106 | D3 | semidirect |
| 25. C3×#106 | C2×C3 | semidirect |
| 27. #810 | C2×C3 | semidirect |
| 71. #106 | C3×D3 | semidirect |
| 130. C32 | #470 | semidirect |
| 159. C3 | #4867 | direct (N × H) |
| 160. C3 | C3×#470 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic12 | 2 |
| C2×C3×ΓL(1,𝔽25) | 2 |
| C3×#897 | 2 |
| C32×#106 | 2 |
| C3×#810 | 2 |
| C3×#470 | 3 |
| #4867 | 3 |