Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
684 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 171 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. #26019927 | C2 | semidirect |
| 5. #26019899 | C2 | semidirect |
| 6. #26019884 | C2 | semidirect |
| 7. #26019848 | C2 | semidirect |
| 160. C89 | #19751 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030993 | 2 |
| #26030799 | 2 |
| #26030633 | 2 |
| #26019927 | 2 |
| #26019899 | 2 |
| #26019884 | 2 |
| #26019848 | 2 |
| #26018555 | 2 |
| C89×#3185 | 2 |
| #19751 | 89 |