Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
211 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 211 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 44. C3×Dic6 | Q8 | semidirect |
| 112. Dic6 | Dic6 | semidirect |
| 156. C32 | #477 | semidirect |
| 188. C3 | #4793 | semidirect |
| 189. C3 | #4875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63919 | 2 |
| #63843 | 2 |
| #63641 | 2 |
| C3×#818 | 2 |
| C3×#816 | 2 |
| #63576 | 2 |
| #63565 | 2 |
| #4875 | 3 |
| #4793 | 3 |