Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
173 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 173 conjugacy classes of subgroups — too many to draw. Only its 62 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×C4×D3 | C2 | semidirect |
| 3. C32×C22⋊C4 | C2 | semidirect |
| 4. C3×#217 | C2 | semidirect |
| 5. C3×(C2×D3)⋊C4 | C2 | semidirect |
| 6. C3×C4⋊Dic3 | C2 | semidirect |
| 7. C3×Dic3⋊C4 | C2 | semidirect |
| 9. #883 | C3 | direct (N × H) |
| 22. C2×C4×D3 | C2×C3 | semidirect |
| 28. C3×C22⋊C4 | D3 | semidirect |
| 29. C3×C22⋊C4 | C2×C3 | semidirect |
| 30. #217 | C2×C3 | semidirect |
| 31. (C2×D3)⋊C4 | C2×C3 | semidirect |
| 32. C4⋊Dic3 | C2×C3 | semidirect |
| 33. Dic3⋊C4 | C2×C3 | semidirect |
| 79. C22⋊C4 | C3×D3 | semidirect |
| 110. C32 | #123 | semidirect |
| 147. C3 | #883 | direct (N × H) |
| 148. C3 | C3×#123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#67 | 2 |
| C2×C3×C4×D3 | 2 |
| C32×C22⋊C4 | 2 |
| C3×#217 | 2 |
| C3×(C2×D3)⋊C4 | 2 |
| C3×C4⋊Dic3 | 2 |
| C3×Dic3⋊C4 | 2 |
| C3×#123 | 3 |
| #883 | 3 |