Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
215 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 215 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 |
|---|---|---|
| 159. C32 | #479 | semidirect |
| 190. C3 | #4796 | semidirect |
| 191. C3 | #4799 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C3⋊Dic3 | 2 |
| #63872 | 2 |
| C3×#835 | 2 |
| #63575 | 2 |
| #63573 | 2 |
| #63572 | 2 |
| #4799 | 3 |
| #4796 | 3 |