Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
236 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 236 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 |
|---|---|---|
| 13. C3×Dic12 | C4 | semidirect |
| 54. Dic12 | Dic3 | semidirect |
| 112. C32 | #441 | semidirect |
| 134. C3 | #4853 | semidirect |
| 135. 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 |
| #63843 | 2 |
| #63642 | 2 |
| C3×#817 | 2 |
| #63565 | 2 |
| #5184 | 3 |
| #4853 | 3 |