Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
480 conjugacy classes of subgroups.
The subgroup lattice has 350 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#19151380 | C2 | semidirect |
| 2. C2×#19151356 | C2 | semidirect |
| 3. #26018243 | C2 | direct (N × H) |
| 8. #19151380 | C22 | semidirect |
| 10. #19151356 | C22 | semidirect |
| 173. C2×C89 | #1341 | semidirect |
| 179. C89 | C2×#1341 | semidirect |
| 347. C2 | #26018243 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151380 | 2 |
| C2×#19151356 | 2 |
| #26018243 | 2 |
| C2×#469×C89 | 2 |
| C2×#1341 | 89 |