Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
147 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 147 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. C2×C3×Dic6 | C2 | semidirect |
| 3. C2×C32×C8 | C2 | semidirect |
| 4. C3×#204 | C2 | direct (N × H) |
| 6. C2×#204 | C3 | direct (N × H) |
| 13. C3×Dic6 | C22 | semidirect |
| 14. C32×C8 | C22 | semidirect |
| 18. C2×Dic6 | C2×C3 | semidirect |
| 21. C2×C3×C8 | D3 | semidirect |
| 22. C2×C3×C8 | C2×C3 | semidirect |
| 23. #204 | C2×C3 | direct (N × H) |
| 45. Dic6 | C22×C3 | semidirect |
| 47. C3×C8 | C2×D3 | semidirect |
| 48. C3×C8 | C22×C3 | semidirect |
| 49. C2×C32 | SD16 | semidirect |
| 55. C2×C8 | C3×D3 | semidirect |
| 71. C32 | C2×SD16 | semidirect |
| 79. C8 | C2×C3×D3 | semidirect |
| 83. C2×C3 | #204 | direct (N × H) |
| 84. C2×C3 | C3×SD16 | semidirect |
| 95. C3 | C2×#204 | direct (N × H) |
| 96. C3 | C2×C3×SD16 | semidirect |
| 98. C2 | C3×#204 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D12 | 2 |
| C2×C3×Dic6 | 2 |
| C2×C32×C8 | 2 |
| C3×#204 | 2 |
| C2×C3×SD16 | 3 |
| C2×#204 | 3 |