Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
254 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 3. C2×C3×Dic12 | C2 | semidirect |
| 4. C3×#817 | C2 | semidirect |
| 5. C3×#816 | C2 | semidirect |
| 7. #5137 | C3 | direct (N × H) |
| 23. C2×Dic12 | C2×C3 | semidirect |
| 26. #817 | C2×C3 | semidirect |
| 27. #816 | C2×C3 | semidirect |
| 138. C32 | #470 | semidirect |
| 168. C3 | #5137 | direct (N × H) |
| 169. C3 | C3×#470 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×M16 | 2 |
| C3×#924 | 2 |
| C2×C3×Dic12 | 2 |
| C3×#817 | 2 |
| C3×#816 | 2 |
| C3×#470 | 3 |
| #5137 | 3 |