Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
914 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 914 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 3. #26018161 | C2 | semidirect |
| 4. #26018160 | C2 | semidirect |
| 5. C89×#1306 | C2 | semidirect |
| 12. #19151560 | C4 | semidirect |
| 14. C22⋊C8×D89 | C4 | semidirect |
| 174. #1306 | D89 | semidirect |
| 175. C89 | #8115 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #407×D89 | 2 |
| #26022632 | 2 |
| #26018161 | 2 |
| #26018160 | 2 |
| C89×#1306 | 2 |
| #8115 | 89 |