Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1188 conjugacy classes of subgroups; only the 311 normal subgroups are shown.
This group has 1188 conjugacy classes of subgroups — too many to draw. Only its 311 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 |
|---|---|---|
| 1. #26028716 | C2 | semidirect |
| 2. #26021927 | C2 | semidirect |
| 3. #26021917 | C2 | semidirect |
| 10. C2×2−1+4×C89 | C4 | semidirect |
| 14. #536×C89 | C4 | semidirect |
| 17. C2×C4⋊Q8×C89 | C4 | semidirect |
| 18. C4×#41×C89 | C4 | semidirect |
| 140. C89 | #33360 | semidirect |
| 141. C2×2−1+4 | Dic89 | semidirect |
| 145. #536 | Dic89 | semidirect |
| 148. C2×C4⋊Q8 | Dic89 | semidirect |
| 150. C4×#41 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028716 | 2 |
| #26021927 | 2 |
| #26021917 | 2 |
| C89×#3499 | 2 |
| #33360 | 89 |