Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
242 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 242 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 |
| 55. Dic12 | Dic3 | semidirect |
| 60. C3⋊Dic3 | Q16 | semidirect |
| 121. C32 | C4×Q16 | semidirect |
| 148. C3 | #4873 | semidirect |
| 149. C3 | Dic3×Q16 | 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 |
| C8×C3⋊Dic3 | 2 |
| C3×#818 | 2 |
| #63565 | 2 |
| Dic3×Q16 | 3 |
| #4873 | 3 |