Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
173 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 173 conjugacy classes of subgroups — too many to draw. Only its 66 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. C22×C3×Dic3 | C2 | semidirect |
| 3. C32×C22⋊C4 | C2 | semidirect |
| 4. C3×(C2×D3)⋊C4 | C2 | semidirect |
| 5. C3×C4⋊Dic3 | C2 | semidirect |
| 7. #886 | C3 | direct (N × H) |
| 18. C22×Dic3 | C2×C3 | semidirect |
| 22. C3×C22⋊C4 | D3 | semidirect |
| 23. C3×C22⋊C4 | C2×C3 | semidirect |
| 24. (C2×D3)⋊C4 | C2×C3 | semidirect |
| 25. C4⋊Dic3 | C2×C3 | semidirect |
| 59. C22⋊C4 | C3×D3 | semidirect |
| 80. C32 | #123 | semidirect |
| 108. C3 | #886 | direct (N × H) |
| 109. 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 |
| C22×C3×Dic3 | 2 |
| C32×C22⋊C4 | 2 |
| C3×(C2×D3)⋊C4 | 2 |
| C3×C4⋊Dic3 | 2 |
| C3×#123 | 3 |
| #886 | 3 |