Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
458 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 135 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. C2×#19151422 | C2 | semidirect |
| 4. #26018352 | C2 | semidirect |
| 12. C22⋊#13083549 | C4 | semidirect |
| 25. C2×#13083549 | C2×C4 | semidirect |
| 103. C22×C89 | #365 | semidirect |
| 124. C89 | #12929 | semidirect |
| 222. C22 | #19151422 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667944 | 2 |
| C2×#19151422 | 2 |
| #26021863 | 2 |
| #26018352 | 2 |
| C89×#1810 | 2 |
| #12929 | 89 |