Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
1800 conjugacy classes of subgroups.
The subgroup lattice has 170 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C11 | C25 |
| commutator | C22 | C24×C4×C11 |
| Frattini, cosocle | C23 | C25×C11 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C11×#564 | C4 | semidirect |
| 43. #34526 | C11 | direct (N × H) |
| 79. #564 | C4×C11 | semidirect |
| 144. C11 | #34526 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C11×#564 | 2 |
| C11×#2382 | 2 |
| C11×#2370 | 2 |
| C11×#2336 | 2 |
| C4×C11×#125 | 2 |
| #34526 | 11 |