Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
121 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 121 conjugacy classes of subgroups — too many to draw. Only its 38 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. C32×C22⋊C4 | C2 | semidirect |
| 3. C3×#217 | C2 | semidirect |
| 5. #806 | C3 | direct (N × H) |
| 7. C22×C3×D3 | C4 | semidirect |
| 12. C2×C3×Dic3 | C4 | semidirect |
| 17. C3×C22⋊C4 | D3 | semidirect |
| 18. C3×C22⋊C4 | C2×C3 | semidirect |
| 19. #217 | C2×C3 | semidirect |
| 34. C22×D3 | C3×C4 | semidirect |
| 45. C2×Dic3 | C3×C4 | semidirect |
| 53. C22⋊C4 | C3×D3 | semidirect |
| 77. C32 | #99 | semidirect |
| 109. C3 | #806 | direct (N × H) |
| 110. C3 | C3×#99 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#67 | 2 |
| C32×C22⋊C4 | 2 |
| C3×#217 | 2 |
| C3×#99 | 3 |
| #806 | 3 |