Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
233 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 233 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 |
|---|---|---|
| 4. C3×#817 | C2 | semidirect |
| 5. C3×#816 | C2 | semidirect |
| 7. #4721 | C3 | direct (N × H) |
| 26. #817 | C2×C3 | semidirect |
| 27. #816 | C2×C3 | semidirect |
| 135. C32 | #483 | semidirect |
| 168. C3 | #4721 | direct (N × H) |
| 169. C3 | C3×#483 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4⋊Dic3 | 2 |
| C3×#924 | 2 |
| C32×C22⋊C8 | 2 |
| C3×#817 | 2 |
| C3×#816 | 2 |
| C3×#483 | 3 |
| #4721 | 3 |