Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
3006 conjugacy classes of subgroups.
The subgroup lattice has 222 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C25×C47 | D4 |
| commutator | C4 | C22×C42×C47 |
| Frattini, cosocle | C22×C4 | C24×C47 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C25×C47 ◁ C24×C4×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×C47×#340 | C2 | direct (N × H) |
| 7. C23×C8×C47 | C4 | semidirect |
| 11. C22×C4⋊C4×C47 | C4 | semidirect |
| 13. C47×#340 | C22 | direct (N × H) |
| 27. C22×C8×C47 | C2×C4 | semidirect |
| 32. C2×C4⋊C4×C47 | C2×C4 | semidirect |
| 58. C2×C8×C47 | C22×C4 | semidirect |
| 61. C4⋊C4×C47 | C22×C4 | semidirect |
| 88. C22×#340 | C47 | direct (N × H) |
| 89. C22×C47 | #340 | direct (N × H) |
| 107. C2×#340 | C2×C47 | direct (N × H) |
| 108. C2×C47 | C2×#340 | direct (N × H) |
| 117. C23×C8 | C4×C47 | semidirect |
| 121. C22×C4⋊C4 | C4×C47 | semidirect |
| 123. #340 | C22×C47 | direct (N × H) |
| 124. C47 | C22×#340 | direct (N × H) |
| 138. C22×C8 | C2×C4×C47 | semidirect |
| 143. C2×C4⋊C4 | C2×C4×C47 | semidirect |
| 169. C2×C8 | C22×C4×C47 | semidirect |
| 172. C4⋊C4 | C22×C4×C47 | semidirect |
| 199. C22 | C47×#340 | direct (N × H) |
| 215. C2 | C2×C47×#340 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C8×C47 | 2 |
| C23×C4⋊C4×C47 | 2 |
| C2×C47×#340 | 2 |
| C22×#340 | 47 |