Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
234 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 7. #4853 | C3 | direct (N × H) |
| 15. C3×Dic12 | C4 | semidirect |
| 53. Dic12 | C3×C4 | semidirect |
| 110. C32 | #441 | semidirect |
| 132. C3 | #4853 | direct (N × H) |
| 133. C3 | C3×#441 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic12 | 2 |
| C3×#887 | 2 |
| C32×#106 | 2 |
| C3×#815 | 2 |
| C3×#810 | 2 |
| C3×#441 | 3 |
| #4853 | 3 |