Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
169 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 169 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 |
|---|---|---|
| 4. C3×Dic3⋊C4 | C2 | semidirect |
| 5. C3×C4×Dic3 | C2 | semidirect |
| 7. #877 | C3 | direct (N × H) |
| 10. C2×C3×Dic3 | C4 | semidirect |
| 23. Dic3⋊C4 | C2×C3 | semidirect |
| 24. C4×Dic3 | C2×C3 | semidirect |
| 43. C2×Dic3 | C3×C4 | semidirect |
| 73. C32 | #117 | semidirect |
| 97. C3 | #877 | direct (N × H) |
| 98. C3 | C3×#117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Dic3 | 2 |
| C32×C22⋊C4 | 2 |
| C3×#217 | 2 |
| C3×Dic3⋊C4 | 2 |
| C3×C4×Dic3 | 2 |
| C3×#117 | 3 |
| #877 | 3 |