Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
464 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26021943 | C2 | semidirect |
| 3. #26021901 | C2 | semidirect |
| 4. #26020302 | C2 | semidirect |
| 5. C89×#1757 | C2 | semidirect |
| 6. C22×D712 | C4 | semidirect |
| 13. #19151636 | C4 | semidirect |
| 14. #19151604 | C4 | semidirect |
| 171. #1757 | D89 | semidirect |
| 172. C89 | #13234 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029900 | 2 |
| #26021943 | 2 |
| #26021901 | 2 |
| #26020302 | 2 |
| C89×#1757 | 2 |
| #13234 | 89 |