Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
257 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 257 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 2. C2×C3×#216 | C2 | semidirect |
| 5. C3×#835 | C2 | semidirect |
| 6. C3×#810 | C2 | semidirect |
| 7. C3×#808 | C2 | semidirect |
| 9. #5052 | C3 | direct (N × H) |
| 29. C2×#216 | C2×C3 | semidirect |
| 35. #835 | C2×C3 | semidirect |
| 36. #810 | C2×C3 | semidirect |
| 37. #808 | C2×C3 | semidirect |
| 190. C32 | #470 | semidirect |
| 230. C3 | #5052 | direct (N × H) |
| 231. C3 | C3×#470 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C22⋊Q8 | 2 |
| C2×C3×#216 | 2 |
| C3×#924 | 2 |
| C2×C3×#208 | 2 |
| C3×#835 | 2 |
| C3×#810 | 2 |
| C3×#808 | 2 |
| C3×#470 | 3 |
| #5052 | 3 |