Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
648 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26018879 | C2 | semidirect |
| 3. #26018788 | C2 | semidirect |
| 4. #26018713 | C2 | semidirect |
| 5. C89×#1991 | C2 | semidirect |
| 6. C89⋊#564 | C4 | semidirect |
| 7. #19152352 | C4 | semidirect |
| 8. #19152346 | C4 | semidirect |
| 181. #1991 | D89 | semidirect |
| 185. C89 | #8529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034708 | 2 |
| #26018879 | 2 |
| #26018788 | 2 |
| #26018713 | 2 |
| C89×#1991 | 2 |
| #8529 | 89 |