Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
220 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 1. C32×#125 | C2 | semidirect |
| 3. C3×#810 | C2 | semidirect |
| 5. C3×C4×C3⋊C8 | C2 | semidirect |
| 7. #5068 | C3 | direct (N × H) |
| 16. C3×#125 | D3 | semidirect |
| 17. C3×#125 | C2×C3 | semidirect |
| 23. #810 | C2×C3 | semidirect |
| 25. C4×C3⋊C8 | C2×C3 | semidirect |
| 59. #125 | C3×D3 | semidirect |
| 111. C32 | #488 | semidirect |
| 136. C3 | #5068 | direct (N × H) |
| 137. C3 | C3×#488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#125 | 2 |
| C3×#875 | 2 |
| C3×#810 | 2 |
| C3×#809 | 2 |
| C3×C4×C3⋊C8 | 2 |
| C3×#488 | 3 |
| #5068 | 3 |