Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
2118 conjugacy classes of subgroups.
The subgroup lattice has 144 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C22×C16×C47 | C22 |
| commutator | C2 | C24×C8×C47 |
| Frattini, cosocle | C8 | C25×C47 |
| socle | C23×C47 | C22×C8 |
| prime radical | C22×#41×C47 | C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C16×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C47×#504 | C2 | direct (N × H) |
| 3. C22×M32×C47 | C2 | semidirect |
| 4. C23×C16×C47 | C2 | semidirect |
| 10. C47×#504 | C22 | direct (N × H) |
| 11. C2×M32×C47 | C22 | semidirect |
| 14. C22×C16×C47 | C22 | semidirect |
| 27. M32×C47 | C23 | semidirect |
| 30. C2×C16×C47 | C23 | semidirect |
| 61. C22×#504 | C47 | direct (N × H) |
| 63. C22×C47 | #504 | direct (N × H) |
| 70. C2×#504 | C2×C47 | direct (N × H) |
| 71. C22×M32 | C2×C47 | semidirect |
| 72. C23×C16 | C2×C47 | semidirect |
| 74. C2×C47 | C2×#504 | direct (N × H) |
| 81. #504 | C22×C47 | direct (N × H) |
| 82. C2×M32 | C22×C47 | semidirect |
| 85. C22×C16 | C22×C47 | semidirect |
| 86. C47 | C22×#504 | direct (N × H) |
| 99. M32 | C23×C47 | semidirect |
| 102. C2×C16 | C23×C47 | semidirect |
| 134. C22 | C47×#504 | direct (N × H) |
| 141. C2 | C2×C47×#504 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#131×C47 | 2 |
| C2×C47×#504 | 2 |
| C22×M32×C47 | 2 |
| C23×C16×C47 | 2 |
| C22×#504 | 47 |