Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
624 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 95 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. #26021917 | C2 | semidirect |
| 3. #26020215 | C2 | semidirect |
| 4. #26018381 | C2 | semidirect |
| 5. C89×#2980 | C2 | semidirect |
| 8. #19151780 | C4 | semidirect |
| 10. #19151770 | C4 | semidirect |
| 196. #2980 | D89 | semidirect |
| 200. C89 | #13053 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029600 | 2 |
| #26021917 | 2 |
| #26020215 | 2 |
| #26018381 | 2 |
| C89×#2980 | 2 |
| #13053 | 89 |