Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
894 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 894 conjugacy classes of subgroups — too many to draw. Only its 155 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. #26021872 | C2 | semidirect |
| 3. #26021867 | C2 | semidirect |
| 4. #26021866 | C2 | semidirect |
| 5. C89×#2115 | C2 | semidirect |
| 14. C2×#15667952 | C22 | semidirect |
| 15. C22×#13083549 | C22 | semidirect |
| 20. C2×M32×C89 | C22 | semidirect |
| 167. #2115 | D89 | semidirect |
| 170. C89 | #12684 | semidirect |
| 181. C2×M32 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034963 | 2 |
| #26021872 | 2 |
| #26021867 | 2 |
| #26021866 | 2 |
| C89×#2115 | 2 |
| #12684 | 89 |