Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
213 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 213 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 40. #634 | Q8 | semidirect |
| 157. C32 | #477 | semidirect |
| 189. C3 | #4850 | semidirect |
| 190. C3 | #4875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63918 | 2 |
| #63844 | 2 |
| #63643 | 2 |
| C3×#818 | 2 |
| C3×Dic3⋊C8 | 2 |
| #63575 | 2 |
| #63567 | 2 |
| #4875 | 3 |
| #4850 | 3 |