Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
3070 conjugacy classes of subgroups.
The subgroup lattice has 300 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C47 | C23 |
| commutator | C22 | C22×C42×C47 |
| Frattini, cosocle | C24 | C24×C47 |
| socle | C24×C47 | C24 |
| prime radical | C25×C47 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C47×C4⋊#95 | C2 | semidirect |
| 5. C4×#95×C47 | C2 | semidirect |
| 10. C2×#117×C47 | C4 | semidirect |
| 14. C22×C42×C47 | C4 | semidirect |
| 35. C2×C4⋊C4×C47 | C2×C4 | semidirect |
| 46. C2×C42×C47 | C2×C4 | semidirect |
| 110. C2×C4×C47 | #95 | semidirect |
| 121. C2×C4×C47 | #117 | semidirect |
| 122. #13756 | C47 | direct (N × H) |
| 145. C4⋊#95 | C2×C47 | semidirect |
| 147. C4×#95 | C2×C47 | semidirect |
| 159. C2×#117 | C4×C47 | semidirect |
| 163. C22×C42 | C4×C47 | semidirect |
| 168. C47 | #13756 | direct (N × H) |
| 185. C2×C4⋊C4 | C2×C4×C47 | semidirect |
| 196. C2×C42 | C2×C4×C47 | semidirect |
| 260. C2×C4 | #95×C47 | semidirect |
| 271. C2×C4 | #117×C47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#117×C47 | 2 |
| C23×C42×C47 | 2 |
| C47×C4⋊#95 | 2 |
| C47×C22⋊#95 | 2 |
| C4×#95×C47 | 2 |
| #13756 | 47 |