Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
716 conjugacy classes of subgroups.
The subgroup lattice has 162 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C4×C47 | C22×C42 |
| commutator | C4 | C22×C42×C47 |
| Frattini, cosocle | C2×C8 | C24×C47 |
| socle | C2×C47 | C22×#97 |
| prime radical | C2×#41×C47 | C2×C4 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C4×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C47×#2110 | C2 | semidirect |
| 4. C2×C47×#347 | C2 | semidirect |
| 8. C47×#504 | C4 | semidirect |
| 27. M32×C47 | C2×C4 | semidirect |
| 29. C2×C16×C47 | C2×C4 | semidirect |
| 69. #33329 | C47 | direct (N × H) |
| 80. #2110 | C2×C47 | semidirect |
| 81. C2×#347 | C2×C47 | semidirect |
| 88. #504 | C4×C47 | semidirect |
| 96. C47 | #33329 | direct (N × H) |
| 108. M32 | C2×C4×C47 | semidirect |
| 110. C2×C16 | C2×C4×C47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C47×#3407 | 2 |
| C47×#2875 | 2 |
| C47×#2110 | 2 |
| C2×C47×#347 | 2 |
| #33329 | 47 |