Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
728 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 179 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. #26030970 | C2 | semidirect |
| 3. #26030646 | C2 | semidirect |
| 4. #26030633 | C2 | semidirect |
| 5. #26019905 | C2 | semidirect |
| 6. #26019898 | C2 | semidirect |
| 7. #26019891 | C2 | semidirect |
| 8. #26019864 | C2 | semidirect |
| 9. C89×#1455 | C2 | semidirect |
| 167. #1455 | D89 | semidirect |
| 168. C89 | #19754 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030990 | 2 |
| #26030970 | 2 |
| #26030646 | 2 |
| #26030633 | 2 |
| #26019905 | 2 |
| #26019898 | 2 |
| #26019891 | 2 |
| #26019864 | 2 |
| C89×#1455 | 2 |
| #19754 | 89 |