Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
238 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 118 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 |
|---|---|---|
| 4. C3×#822 | C2 | semidirect |
| 6. #5124 | C3 | direct (N × H) |
| 25. #822 | C2×C3 | semidirect |
| 139. C32 | #430 | semidirect |
| 171. C3 | #5124 | direct (N × H) |
| 172. C3 | C3×#430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×M16 | 2 |
| C2×C3×#208 | 2 |
| C3×#822 | 2 |
| C3×#430 | 3 |
| #5124 | 3 |