Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
169 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 169 conjugacy classes of subgroups — too many to draw. Only its 58 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. C3×Dic3⋊C4 | C2 | semidirect |
| 4. C3×C4×Dic3 | C2 | semidirect |
| 5. Dic3⋊Dic3 | C2 | semidirect |
| 7. Dic32 | C2 | semidirect |
| 17. #624 | C4 | semidirect |
| 29. Dic3⋊C4 | D3 | semidirect |
| 32. C4×Dic3 | D3 | semidirect |
| 100. C32 | #117 | semidirect |
| 132. C3 | #872 | semidirect |
| 133. C3 | #892 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#624 | 2 |
| #3752 | 2 |
| C3×Dic3⋊C4 | 2 |
| C3×C4×Dic3 | 2 |
| Dic3⋊Dic3 | 2 |
| #3722 | 2 |
| Dic32 | 2 |
| #892 | 3 |
| #872 | 3 |