Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
462 conjugacy classes of subgroups.
The subgroup lattice has 112 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C16×C47 | C24 |
| commutator | C2 | C23×C16×C47 |
| Frattini, cosocle | C16 | C24×C47 |
| socle | C2×C47 | C23×C16 |
| prime radical | C2×#41×C47 | C8 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C16×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C47×#2258 | C2 | semidirect |
| 3. C2×C47×M64 | C2 | semidirect |
| 10. C47×M64 | C22 | semidirect |
| 11. C2×C32×C47 | C22 | semidirect |
| 46. #33974 | C47 | direct (N × H) |
| 54. #2258 | C2×C47 | semidirect |
| 55. C2×M64 | C2×C47 | semidirect |
| 65. M64 | C22×C47 | semidirect |
| 66. C2×C32 | C22×C47 | semidirect |
| 67. C47 | #33974 | 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 |
| C47×#2258 | 2 |
| C2×C47×M64 | 2 |
| #33974 | 47 |