Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
890 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 890 conjugacy classes of subgroups — too many to draw. Only its 135 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. #26021989 | C2 | semidirect |
| 3. #26021960 | C2 | semidirect |
| 4. #26020298 | C2 | semidirect |
| 5. C89×#2113 | C2 | semidirect |
| 11. #19152398 | C4 | semidirect |
| 14. #19151636 | C22 | semidirect |
| 21. C2×M32×C89 | C22 | semidirect |
| 22. C22×C16×C89 | C22 | semidirect |
| 171. #2113 | D89 | semidirect |
| 173. C89 | #12745 | semidirect |
| 183. C2×M32 | C2×D89 | semidirect |
| 184. C22×C16 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26035026 | 2 |
| #26021989 | 2 |
| #26021960 | 2 |
| #26020298 | 2 |
| C89×#2113 | 2 |
| #12745 | 89 |