Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
133 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 133 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 |
|---|---|---|
| 1. C32×C4⋊C4 | C2 | semidirect |
| 5. C3×C4⋊Dic3 | C2 | semidirect |
| 6. C3×Dic3⋊C4 | C2 | semidirect |
| 7. C3×C4×Dic3 | C2 | semidirect |
| 9. #898 | C3 | direct (N × H) |
| 20. C3×C4⋊C4 | D3 | semidirect |
| 21. C3×C4⋊C4 | C2×C3 | semidirect |
| 29. C4⋊Dic3 | C2×C3 | semidirect |
| 30. Dic3⋊C4 | C2×C3 | semidirect |
| 31. C4×Dic3 | C2×C3 | semidirect |
| 66. C4⋊C4 | C3×D3 | semidirect |
| 95. C32 | #126 | semidirect |
| 125. C3 | #898 | direct (N × H) |
| 126. C3 | C3×#126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4⋊C4 | 2 |
| C3×(C2×D3)⋊C4 | 2 |
| C3×C4⋊Dic3 | 2 |
| C3×Dic3⋊C4 | 2 |
| C3×C4×Dic3 | 2 |
| C3×#126 | 3 |
| #898 | 3 |