Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
736 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26021946 | C2 | semidirect |
| 3. #26021905 | C2 | semidirect |
| 4. #26020802 | C2 | semidirect |
| 5. #26020772 | C2 | semidirect |
| 10. #19152351 | C4 | semidirect |
| 14. #19152279 | C4 | semidirect |
| 284. C89 | #12757 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034501 | 2 |
| #26021946 | 2 |
| #26021905 | 2 |
| #26020802 | 2 |
| #26020772 | 2 |
| #26020671 | 2 |
| C89×#2120 | 2 |
| #12757 | 89 |