Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
2582 conjugacy classes of subgroups.
The subgroup lattice has 432 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C25×C89 | C23 |
| commutator | C23 | C2×C42×C89 |
| Frattini, cosocle | C25 | C23×C89 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C25×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 12. C2×#95×C89 | C4 | semidirect |
| 206. #7556 | C89 | direct (N × H) |
| 219. C89 | #7556 | direct (N × H) |
| 228. C2×#95 | C4×C89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#95×C89 | 2 |
| #7556 | 89 |