Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
231 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 231 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D32 |
| commutator, hypocenter | C32 | C2×C42 |
| Frattini | C22 | C2×D32 |
| Fitting | C2×C32×C4 | C22 |
| socle, cosocle | C22×C32 | C23 |
| prime radical | C22×C3×D3 | C22 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C4×C3⋊Dic3 | C2 | semidirect |
| 4. C3×C4×Dic3 | C2 | semidirect |
| 5. Dic32 | C2 | semidirect |
| 13. C3×C4×D3 | C4 | semidirect |
| 14. D3×Dic3 | C4 | direct (N × H) |
| 25. C4×Dic3 | D3 | direct (N × H) |
| 29. C32×C4 | C2×C4 | semidirect |
| 30. C3⋊Dic3 | C2×C4 | semidirect |
| 31. C3×Dic3 | C2×C4 | semidirect |
| 32. C3×Dic3 | C2×C4 | semidirect |
| 49. C4×D3 | Dic3 | direct (N × H) |
| 52. C3×D3 | C42 | semidirect |
| 68. C3×C4 | C4×D3 | semidirect |
| 69. C3×C4 | C2×Dic3 | semidirect |
| 73. Dic3 | C4×D3 | direct (N × H) |
| 74. Dic3 | C2×Dic3 | semidirect |
| 75. C32 | C2×C42 | semidirect |
| 90. D3 | C4×Dic3 | direct (N × H) |
| 97. C4 | D3×Dic3 | direct (N × H) |
| 99. C3 | C42×D3 | semidirect |
| 100. C3 | C2×C4×Dic3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D3 | 2 |
| C2×D3×Dic3 | 2 |
| C4×C3⋊Dic3 | 2 |
| C3×C4×Dic3 | 2 |
| Dic32 | 2 |
| C2×C4×Dic3 | 3 |
| C42×D3 | 3 |