Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
834 conjugacy classes of subgroups.
The subgroup lattice has 174 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C4×C16×C47 | C22 |
| commutator | C2 | C22×C4×C8×C47 |
| Frattini, cosocle | C2×C8 | C24×C47 |
| socle | C22×C47 | C23×C8 |
| prime radical | C2×#41×C47 | C2×C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C16×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C47×#2108 | C2 | semidirect |
| 4. C4×M32×C47 | C2 | semidirect |
| 5. C2×C4×C16×C47 | C2 | semidirect |
| 9. C47×#504 | C4 | direct (N × H) |
| 31. M32×C47 | C2×C4 | semidirect |
| 32. C2×C16×C47 | C2×C4 | semidirect |
| 75. C4×#504 | C47 | direct (N × H) |
| 81. C4×C47 | #504 | direct (N × H) |
| 86. #2108 | C2×C47 | semidirect |
| 87. C4×M32 | C2×C47 | semidirect |
| 88. C2×C4×C16 | C2×C47 | semidirect |
| 95. #504 | C4×C47 | direct (N × H) |
| 106. C47 | C4×#504 | direct (N × H) |
| 118. M32 | C2×C4×C47 | semidirect |
| 119. C2×C16 | C2×C4×C47 | semidirect |
| 167. C4 | C47×#504 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C47×#504 | 2 |
| C4×#131×C47 | 2 |
| C47×#2108 | 2 |
| C4×M32×C47 | 2 |
| C2×C4×C16×C47 | 2 |
| C4×#504 | 47 |