Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1154 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 115 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. C2×#19151394 | C2 | semidirect |
| 3. #26020180 | C2 | semidirect |
| 4. C89×#1785 | C2 | semidirect |
| 14. C2×#15667931 | C22 | semidirect |
| 19. C2×#101×C89 | C22 | semidirect |
| 210. #1785 | D89 | semidirect |
| 211. C89 | #12703 | semidirect |
| 223. C2×#101 | 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 |
| C2×#19151394 | 2 |
| #26020180 | 2 |
| C89×#1785 | 2 |
| #12703 | 89 |