Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
217 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 217 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 |
|---|---|---|
| 4. C3×#818 | C2 | semidirect |
| 5. C3×#817 | C2 | semidirect |
| 6. C3×#816 | C2 | semidirect |
| 7. C3×#816 | C2 | semidirect |
| 9. #4723 | C3 | direct (N × H) |
| 32. #818 | C2×C3 | semidirect |
| 33. #817 | C2×C3 | semidirect |
| 34. #816 | C2×C3 | semidirect |
| 35. #816 | C2×C3 | semidirect |
| 170. C32 | #485 | semidirect |
| 208. C3 | #4723 | direct (N × H) |
| 209. C3 | C3×#485 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#926 | 2 |
| C3×#924 | 2 |
| C32×C22⋊C8 | 2 |
| C3×#818 | 2 |
| C3×#817 | 2 |
| C3×#816 | 2 |
| C3×#485 | 3 |
| #4723 | 3 |