Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
201 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 201 conjugacy classes of subgroups — too many to draw. Only its 60 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 |
|---|---|---|
| 160. C32 | #491 | semidirect |
| 193. C3 | #4703 | semidirect |
| 194. C3 | #4797 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63869 | 2 |
| #63866 | 2 |
| #63643 | 2 |
| C3×#816 | 2 |
| C3×#815 | 2 |
| #63567 | 2 |
| #63566 | 2 |
| #4797 | 3 |
| #4703 | 3 |