Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
218 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 218 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 |
|---|---|---|
| 2. C2×C3×Dic12 | C2 | semidirect |
| 3. C3×#827 | C2 | direct (N × H) |
| 4. C2×C3×C3⋊C16 | C2 | semidirect |
| 6. C2×#827 | C3 | direct (N × H) |
| 13. C3×Dic12 | C22 | semidirect |
| 14. C3×C3⋊C16 | C22 | semidirect |
| 19. C2×Dic12 | C2×C3 | semidirect |
| 22. #827 | C2×C3 | direct (N × H) |
| 23. C2×C3⋊C16 | C2×C3 | semidirect |
| 51. Dic12 | C22×C3 | semidirect |
| 53. C3⋊C16 | C22×C3 | semidirect |
| 89. C2×C32 | SD32 | semidirect |
| 116. C32 | C2×SD32 | semidirect |
| 131. C2×C3 | #827 | direct (N × H) |
| 132. C2×C3 | C3×SD32 | semidirect |
| 142. C3 | C2×#827 | direct (N × H) |
| 143. C3 | C2×C3×SD32 | semidirect |
| 145. C2 | C3×#827 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D8 | 2 |
| C2×C3×Dic12 | 2 |
| C3×#827 | 2 |
| C2×C3×C3⋊C16 | 2 |
| C2×C3×SD32 | 3 |
| C2×#827 | 3 |