Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
235 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 235 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 7. #4849 | C3 | direct (N × H) |
| 65. C32×C4 | Q16 | semidirect |
| 127. C3×C4 | Dic12 | semidirect |
| 128. C3×C4 | C3×Q16 | semidirect |
| 136. C32 | #462 | semidirect |
| 162. C4 | C3×Dic12 | semidirect |
| 166. C3 | #4849 | direct (N × H) |
| 167. C3 | C3×#462 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic12 | 2 |
| C3×#869 | 2 |
| C3×C4×Dic6 | 2 |
| C32×C4⋊C8 | 2 |
| C3×#816 | 2 |
| C3×#462 | 3 |
| #4849 | 3 |