Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
215 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 215 conjugacy classes of subgroups — too many to draw. Only its 102 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. C3×#217 | C2 | semidirect |
| 4. C3×C4⋊Dic3 | C2 | semidirect |
| 5. C3×C4×Dic3 | C2 | semidirect |
| 7. D4×Dic3 | C3 | direct (N × H) |
| 9. C32×D4 | C4 | semidirect |
| 19. C22×Dic3 | C2×C3 | semidirect |
| 23. #217 | C2×C3 | semidirect |
| 24. C4⋊Dic3 | C2×C3 | semidirect |
| 25. C4×Dic3 | C2×C3 | semidirect |
| 28. C22×C32 | C2×C4 | semidirect |
| 30. C32×C4 | C2×C4 | semidirect |
| 33. C3×Dic3 | D4 | direct (N × H) |
| 39. C3×D4 | Dic3 | direct (N × H) |
| 40. C3×D4 | C3×C4 | semidirect |
| 69. C22×C3 | C2×Dic3 | semidirect |
| 70. C22×C3 | C2×C3×C4 | semidirect |
| 77. C3×C4 | C2×Dic3 | semidirect |
| 78. C3×C4 | C2×C3×C4 | semidirect |
| 81. Dic3 | C3×D4 | direct (N × H) |
| 82. C32 | C4×D4 | semidirect |
| 84. D4 | C3×Dic3 | direct (N × H) |
| 104. C22 | C2×C3×Dic3 | semidirect |
| 109. C4 | C2×C3×Dic3 | semidirect |
| 111. C3 | D4×Dic3 | direct (N × H) |
| 112. C3 | C3×C4×D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D4 | 2 |
| C22×C3×Dic3 | 2 |
| C3×#217 | 2 |
| C3×C4⋊Dic3 | 2 |
| C3×C4×Dic3 | 2 |
| C3×C4×D4 | 3 |
| D4×Dic3 | 3 |