Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
334 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 334 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 |
|---|---|---|
| 3. #26018428 | C2 | semidirect |
| 5. #19152155 | C4 | semidirect |
| 8. #19151952 | C4 | semidirect |
| 13. C4×#13083558 | C4 | semidirect |
| 22. #15668004 | C2×C4 | semidirect |
| 34. C4×#10623494 | C2×C4 | semidirect |
| 141. C89 | #13603 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030638 | 2 |
| C2×#19151393 | 2 |
| #26018428 | 2 |
| C2×#355×C89 | 2 |
| #13603 | 89 |