Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
167 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 167 conjugacy classes of subgroups — too many to draw. Only its 82 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. C32×C42 | C2 | semidirect |
| 4. C3×Dic3⋊C4 | C2 | semidirect |
| 5. C3×C4×Dic3 | C2 | semidirect |
| 7. #872 | C3 | direct (N × H) |
| 13. C3×C4×D3 | C4 | semidirect |
| 20. C3×C42 | D3 | semidirect |
| 21. C3×C42 | C2×C3 | semidirect |
| 23. Dic3⋊C4 | C2×C3 | semidirect |
| 24. C4×Dic3 | C2×C3 | semidirect |
| 46. C4×D3 | C3×C4 | semidirect |
| 54. C42 | C3×D3 | semidirect |
| 72. C32 | #117 | semidirect |
| 95. C3 | #872 | direct (N × H) |
| 96. C3 | C3×#117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D3 | 2 |
| C32×C42 | 2 |
| C3×(C2×D3)⋊C4 | 2 |
| C3×Dic3⋊C4 | 2 |
| C3×C4×Dic3 | 2 |
| C3×#117 | 3 |
| #872 | 3 |