Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
778 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 113 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×#19151933 | C2 | semidirect |
| 4. C2×#19151336 | C2 | semidirect |
| 6. #26018130 | C2 | semidirect |
| 7. C89×#1824 | C2 | semidirect |
| 251. #1824 | D89 | semidirect |
| 255. C89 | #9928 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151933 | 2 |
| #26026060 | 2 |
| C2×#19151533 | 2 |
| C2×#19151336 | 2 |
| C2×#19151321 | 2 |
| #26018130 | 2 |
| C89×#1824 | 2 |
| #9928 | 89 |