Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
234 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 13. C3×Dic12 | C4 | semidirect |
| 53. Dic12 | Dic3 | semidirect |
| 110. C32 | #441 | semidirect |
| 132. C3 | #4716 | semidirect |
| 133. C3 | #5184 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic12 | 2 |
| Dic3×Dic6 | 2 |
| #63644 | 2 |
| C3×#815 | 2 |
| #63566 | 2 |
| #5184 | 3 |
| #4716 | 3 |