Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
416 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 71 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. #26018416 | C2 | semidirect |
| 4. #26018414 | C2 | semidirect |
| 5. C89×#2126 | C2 | semidirect |
| 8. #19152148 | C4 | semidirect |
| 11. #19151977 | C4 | semidirect |
| 13. #19151972 | C4 | semidirect |
| 16. C2×C4×#10623494 | C4 | semidirect |
| 176. #2126 | D89 | semidirect |
| 179. C89 | #13583 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030678 | 2 |
| #26021917 | 2 |
| #26018416 | 2 |
| #26018414 | 2 |
| C89×#2126 | 2 |
| #13583 | 89 |