Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
492 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 93 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. #26018764 | C2 | semidirect |
| 5. #26018146 | C2 | semidirect |
| 6. #26018108 | C2 | semidirect |
| 7. C89×#1986 | C2 | semidirect |
| 10. #19151875 | C4 | semidirect |
| 11. #19151800 | C4 | semidirect |
| 184. #1986 | D89 | semidirect |
| 189. C89 | #9327 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030347 | 2 |
| #26022890 | 2 |
| #26018764 | 2 |
| #26018696 | 2 |
| #26018146 | 2 |
| #26018108 | 2 |
| C89×#1986 | 2 |
| #9327 | 89 |