Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
214 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 5. #4556 | C3 | direct (N × H) |
| 9. C2×C32×C8 | C4 | semidirect |
| 14. C3×#208 | C4 | semidirect |
| 47. C2×C3×C8 | Dic3 | semidirect |
| 48. C2×C3×C8 | C3×C4 | semidirect |
| 56. #208 | C3×C4 | semidirect |
| 108. C2×C8 | C3×Dic3 | semidirect |
| 138. C32 | #344 | semidirect |
| 171. C3 | #4556 | direct (N × H) |
| 172. C3 | C3×#344 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×M16 | 2 |
| C3×#926 | 2 |
| C2×C3×#208 | 2 |
| C3×#344 | 3 |
| #4556 | 3 |