Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
458 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26021973 | C2 | semidirect |
| 4. #26021971 | C2 | semidirect |
| 6. #26018353 | C2 | semidirect |
| 7. C89×#1384 | C2 | semidirect |
| 15. #19151857 | C4 | semidirect |
| 170. #1384 | D89 | semidirect |
| 171. C89 | #13075 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033354 | 2 |
| #26029908 | 2 |
| #26021973 | 2 |
| #26021971 | 2 |
| #26020295 | 2 |
| #26018353 | 2 |
| C89×#1384 | 2 |
| #13075 | 89 |