Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
252 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 4. C2×#15667952 | C4 | semidirect |
| 5. C22×#13083549 | C4 | semidirect |
| 10. #19151355 | C4 | semidirect |
| 14. H(3,ℤ/4)×C89 | C4 | semidirect |
| 115. C89 | #7228 | semidirect |
| 126. H(3,ℤ/4) | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021866 | 2 |
| #26020298 | 2 |
| C89×#1812 | 2 |
| #7228 | 89 |