Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1386 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 1386 conjugacy classes of subgroups — too many to draw. Only its 235 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. #26028887 | C2 | semidirect |
| 3. #26021100 | C2 | semidirect |
| 4. #26021090 | C2 | semidirect |
| 5. #26020180 | C2 | semidirect |
| 6. #26020172 | C2 | semidirect |
| 7. C89×#1785 | C2 | semidirect |
| 16. #19151621 | C22 | semidirect |
| 17. C2×#15667931 | C22 | semidirect |
| 18. C2×#15667929 | C22 | semidirect |
| 22. M16×Dic89 | C22 | semidirect |
| 24. C2×#101×C89 | C22 | semidirect |
| 25. C2×#100×C89 | C22 | semidirect |
| 187. #1785 | D89 | semidirect |
| 189. C89 | #21801 | semidirect |
| 201. C2×#101 | C2×D89 | semidirect |
| 205. C2×#100 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152162 | 2 |
| #26028887 | 2 |
| #26021100 | 2 |
| #26021090 | 2 |
| #26020180 | 2 |
| #26020172 | 2 |
| C89×#1785 | 2 |
| #21801 | 89 |