Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
125 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 125 conjugacy classes of subgroups — too many to draw. Only its 54 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. C32×M32 | C2 | semidirect |
| 3. C2×C3×C3⋊C16 | C2 | semidirect |
| 5. #4515 | C3 | direct (N × H) |
| 16. C3×M32 | D3 | semidirect |
| 17. C3×M32 | C2×C3 | semidirect |
| 19. C2×C3⋊C16 | C2×C3 | semidirect |
| 51. M32 | C3×D3 | semidirect |
| 95. C32 | #350 | semidirect |
| 118. C3 | #4515 | direct (N × H) |
| 119. C3 | C3×#350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#901 | 2 |
| C32×M32 | 2 |
| C2×C3×C3⋊C16 | 2 |
| C3×#350 | 3 |
| #4515 | 3 |