Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
130 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 130 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 |
|---|---|---|
| 2. C2×C3×Dic6 | C2 | semidirect |
| 3. C32×M16 | C2 | semidirect |
| 4. C3×Dic12 | C2 | semidirect |
| 5. C3×#204 | C2 | semidirect |
| 7. #909 | C3 | direct (N × H) |
| 20. C2×Dic6 | C2×C3 | semidirect |
| 24. C3×M16 | D3 | semidirect |
| 25. C3×M16 | C2×C3 | semidirect |
| 26. Dic12 | C2×C3 | semidirect |
| 27. #204 | C2×C3 | semidirect |
| 62. M16 | C3×D3 | semidirect |
| 78. C32 | #137 | semidirect |
| 103. C3 | #909 | direct (N × H) |
| 104. C3 | C3×#137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#235 | 2 |
| C2×C3×Dic6 | 2 |
| C32×M16 | 2 |
| C3×Dic12 | 2 |
| C3×#204 | 2 |
| C3×#137 | 3 |
| #909 | 3 |