Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
358 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 119 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. #26022025 | C2 | semidirect |
| 5. #26018349 | C2 | semidirect |
| 6. #26018347 | C2 | semidirect |
| 7. C89×#2155 | C2 | semidirect |
| 11. C2×#15667951 | C4 | semidirect |
| 13. C2×C16×D89 | C4 | semidirect |
| 142. #2155 | D89 | semidirect |
| 147. C89 | #12832 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152016 | 2 |
| #26022025 | 2 |
| #26020299 | 2 |
| #26020295 | 2 |
| #26018349 | 2 |
| #26018347 | 2 |
| C89×#2155 | 2 |
| #12832 | 89 |