Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
558 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26028887 | C2 | semidirect |
| 3. #26020333 | C2 | semidirect |
| 6. #26018160 | C2 | semidirect |
| 7. C89×#1306 | C2 | semidirect |
| 248. #1306 | D89 | semidirect |
| 249. C89 | #9512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028887 | 2 |
| #26024528 | 2 |
| #26020333 | 2 |
| #26018578 | 2 |
| #26018160 | 2 |
| C89×#1306 | 2 |
| #9512 | 89 |