Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
164 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C4 | A4 |
| commutator, hypocenter | C22 | C2×C32×C4 |
| Frattini | C2 | C22×C3×A4 |
| Fitting | C23×C3×C4 | C3 |
| socle | C24×C3 | C2×C3 |
| prime radical | C22×C3×A4 | C2 |
| cosocle | C23 | C22×C32 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C2×C3×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×C4×A4 | C2 | direct (N × H) |
| 3. C23×C3×C4 | C3 | semidirect |
| 4. C2×C4×A4 | C3 | direct (N × H) |
| 5. C2×C3×A4 | C4 | direct (N × H) |
| 13. C22×C3×C4 | C2×C3 | semidirect |
| 14. C4×A4 | C2×C3 | direct (N × H) |
| 16. C3×A4 | C2×C4 | direct (N × H) |
| 18. C23×C4 | C32 | semidirect |
| 22. C23×C3 | C3×C4 | semidirect |
| 24. C2×A4 | C3×C4 | direct (N × H) |
| 32. C2×C3×C4 | A4 | direct (N × H) |
| 39. C22×C4 | C2×C32 | semidirect |
| 48. C22×C3 | C2×C3×C4 | semidirect |
| 50. A4 | C2×C3×C4 | direct (N × H) |
| 53. C3×C4 | C2×A4 | direct (N × H) |
| 58. C23 | C32×C4 | semidirect |
| 65. C2×C4 | C3×A4 | direct (N × H) |
| 71. C2×C3 | C4×A4 | direct (N × H) |
| 80. C22 | C2×C32×C4 | semidirect |
| 83. C4 | C2×C3×A4 | direct (N × H) |
| 85. C3 | C2×C4×A4 | direct (N × H) |
| 89. C2 | C3×C4×A4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×A4 | 2 |
| C3×C4×A4 | 2 |
| C23×C3×C4 | 3 |
| C2×C4×A4 | 3 |
| C2×C32×C4 | 4 |