Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
281 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 281 conjugacy classes of subgroups — too many to draw. Only its 98 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×C4×D3 | C2 | semidirect |
| 3. C32×C22⋊C4 | C2 | semidirect |
| 4. C3×#217 | C2 | semidirect |
| 5. C3×(C2×D3)⋊C4 | C2 | semidirect |
| 7. D3×C22⋊C4 | C3 | direct (N × H) |
| 10. C22×C3×D3 | C4 | semidirect |
| 13. C2×C32×C4 | C22 | semidirect |
| 14. C2×C3×Dic3 | C22 | semidirect |
| 19. C2×C4×D3 | C2×C3 | semidirect |
| 23. C3×C22⋊C4 | D3 | direct (N × H) |
| 24. C3×C22⋊C4 | C2×C3 | semidirect |
| 25. #217 | C2×C3 | semidirect |
| 26. (C2×D3)⋊C4 | C2×C3 | semidirect |
| 28. C22×C32 | C2×C4 | semidirect |
| 33. C2×C3×D3 | C2×C4 | semidirect |
| 46. C22×D3 | C3×C4 | semidirect |
| 52. C2×C3×C4 | C2×D3 | semidirect |
| 53. C2×C3×C4 | C22×C3 | semidirect |
| 54. C2×Dic3 | C22×C3 | semidirect |
| 60. C3×D3 | C22⋊C4 | direct (N × H) |
| 65. C22⋊C4 | C3×D3 | direct (N × H) |
| 76. C22×C3 | C4×D3 | semidirect |
| 77. C22×C3 | C2×C3×C4 | semidirect |
| 83. C2×D3 | C2×C3×C4 | semidirect |
| 90. C32 | C2×C22⋊C4 | semidirect |
| 98. C2×C4 | C2×C3×D3 | semidirect |
| 111. D3 | C3×C22⋊C4 | direct (N × H) |
| 118. C22 | C3×C4×D3 | semidirect |
| 123. C3 | D3×C22⋊C4 | direct (N × H) |
| 124. C3 | C2×C3×C22⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×D3 | 2 |
| C2×C3×C4×D3 | 2 |
| C32×C22⋊C4 | 2 |
| C3×#217 | 2 |
| C3×(C2×D3)⋊C4 | 2 |
| C2×C3×C22⋊C4 | 3 |
| D3×C22⋊C4 | 3 |