Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
726 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. #26022838 | C2 | semidirect |
| 4. #26018106 | C2 | semidirect |
| 5. C89×#1784 | C2 | semidirect |
| 6. C2×#15668001 | C4 | semidirect |
| 11. #19151505 | C4 | semidirect |
| 170. #1784 | D89 | semidirect |
| 173. C89 | #9466 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023906 | 2 |
| #26022838 | 2 |
| #26018782 | 2 |
| #26018106 | 2 |
| C89×#1784 | 2 |
| #9466 | 89 |