Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
464 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 464 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. #26021943 | C2 | semidirect |
| 3. #26021903 | C2 | semidirect |
| 4. #26020052 | C2 | semidirect |
| 5. C89×#1813 | C2 | semidirect |
| 6. C22×D712 | C4 | semidirect |
| 12. #19151636 | C4 | semidirect |
| 13. #19151604 | C4 | semidirect |
| 170. #1813 | 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 |
| #26021903 | 2 |
| #26020052 | 2 |
| C89×#1813 | 2 |
| #13234 | 89 |