Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
866 conjugacy classes of subgroups.
The subgroup lattice has 318 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C47 | C24 |
| commutator | C22 | C23×C8×C47 |
| Frattini, cosocle | C22×C4 | C24×C47 |
| socle | C23×C47 | C23×C4 |
| prime radical | C24×C47 | C22×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C47×#1916 | C2 | semidirect |
| 30. C2×C4⋊C4×C47 | C8 | semidirect |
| 128. #21912 | C47 | direct (N × H) |
| 152. #1916 | C2×C47 | semidirect |
| 179. C47 | #21912 | direct (N × H) |
| 189. C2×C4⋊C4 | C8×C47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C4⋊C4×C47 | 2 |
| C47×#1916 | 2 |
| C47×#1817 | 2 |
| C47×#1797 | 2 |
| C4×C22⋊C8×C47 | 2 |
| #21912 | 47 |