Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
291 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 291 conjugacy classes of subgroups — too many to draw. Only its 114 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×C32×C4 | C2 | semidirect |
| 3. C22×C3×Dic3 | C2 | semidirect |
| 4. C3×(C2×D3)⋊C4 | C2 | direct (N × H) |
| 6. C2×(C2×D3)⋊C4 | C3 | direct (N × H) |
| 10. C22×C3×D3 | C4 | semidirect |
| 13. C2×C32×C4 | C22 | semidirect |
| 15. C2×C3×Dic3 | C22 | semidirect |
| 20. C22×C3×C4 | D3 | semidirect |
| 21. C22×C3×C4 | C2×C3 | semidirect |
| 22. C22×Dic3 | C2×C3 | semidirect |
| 24. (C2×D3)⋊C4 | C2×C3 | direct (N × H) |
| 32. C2×C3×D3 | C2×C4 | semidirect |
| 45. C22×D3 | C3×C4 | semidirect |
| 53. C2×C3×C4 | C2×D3 | semidirect |
| 54. C2×C3×C4 | C22×C3 | semidirect |
| 56. C2×Dic3 | C22×C3 | semidirect |
| 57. C2×C32 | C22⋊C4 | semidirect |
| 64. C22×C4 | C3×D3 | semidirect |
| 85. C2×D3 | C2×C3×C4 | semidirect |
| 91. C32 | C2×C22⋊C4 | semidirect |
| 100. C2×C4 | C2×C3×D3 | semidirect |
| 106. C2×C3 | (C2×D3)⋊C4 | direct (N × H) |
| 107. C2×C3 | C3×C22⋊C4 | semidirect |
| 126. C3 | C2×(C2×D3)⋊C4 | direct (N × H) |
| 127. C3 | C2×C3×C22⋊C4 | semidirect |
| 129. C2 | C3×(C2×D3)⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×D3 | 2 |
| C22×C32×C4 | 2 |
| C22×C3×Dic3 | 2 |
| C3×(C2×D3)⋊C4 | 2 |
| C2×C3×C22⋊C4 | 3 |
| C2×(C2×D3)⋊C4 | 3 |