Order 22784.
1062 conjugacy classes of subgroups.
The subgroup lattice has 352 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C89 | C23 |
| commutator | C22 | C2×C4×C8×C89 |
| Frattini, cosocle | C23×C4 | C23×C89 |
| socle, prime radical | C24×C89 | C22×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 14. #336×C89 | C4 | semidirect |
| 38. C2×C42×C89 | C8 | semidirect |
| 164. #10795 | C89 | direct (N × H) |
| 180. C89 | #10795 | direct (N × H) |
| 190. #336 | C4×C89 | semidirect |
| 214. C2×C42 | C8×C89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C43×C89 | 2 |
| C2×#336×C89 | 2 |
| #10795 | 89 |