Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
331 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 331 conjugacy classes of subgroups — too many to draw. Only its 130 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 | direct (N × H) |
| 5. C2×#217 | C3 | direct (N × H) |
| 7. C23×C32 | C4 | semidirect |
| 11. C2×C3×Dic3 | C22 | semidirect |
| 16. C22×Dic3 | C2×C3 | semidirect |
| 18. #217 | C2×C3 | direct (N × H) |
| 22. C22×C32 | C2×C4 | semidirect |
| 33. C23×C3 | Dic3 | semidirect |
| 34. C23×C3 | C3×C4 | semidirect |
| 42. C2×Dic3 | C22×C3 | semidirect |
| 44. C2×C32 | C22⋊C4 | semidirect |
| 61. C22×C3 | C2×Dic3 | semidirect |
| 64. C22×C3 | C2×C3×C4 | semidirect |
| 70. C32 | C2×C22⋊C4 | semidirect |
| 72. C23 | C3×Dic3 | semidirect |
| 83. C2×C3 | #217 | direct (N × H) |
| 84. C2×C3 | C3×C22⋊C4 | semidirect |
| 92. C22 | C2×C3×Dic3 | semidirect |
| 97. C3 | C2×#217 | direct (N × H) |
| 98. C3 | C2×C3×C22⋊C4 | semidirect |
| 100. C2 | C3×#217 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C32 | 2 |
| C22×C3×Dic3 | 2 |
| C3×#217 | 2 |
| C2×C3×C22⋊C4 | 3 |
| C2×#217 | 3 |