Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
386 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 91 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. #26021960 | C2 | semidirect |
| 3. #26021150 | C2 | semidirect |
| 4. #26018354 | C2 | semidirect |
| 5. C89×#2151 | C2 | semidirect |
| 111. #2151 | D89 | semidirect |
| 115. C89 | #13447 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033388 | 2 |
| #26021960 | 2 |
| #26021150 | 2 |
| #26018354 | 2 |
| C89×#2151 | 2 |
| #13447 | 89 |