Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
734 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 734 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#19151929 | C2 | semidirect |
| 4. #26020336 | C2 | semidirect |
| 5. C2×#19151334 | C2 | semidirect |
| 7. C89×#1294 | C2 | semidirect |
| 257. #1294 | D89 | semidirect |
| 258. C89 | #9926 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151929 | 2 |
| #26026060 | 2 |
| C2×#19151525 | 2 |
| #26020336 | 2 |
| C2×#19151334 | 2 |
| C2×#19151321 | 2 |
| C89×#1294 | 2 |
| #9926 | 89 |