Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
566 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 113 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×#19151418 | C2 | semidirect |
| 3. C2×#19151412 | C2 | semidirect |
| 4. C2×#19151411 | C2 | semidirect |
| 5. #26021967 | C2 | semidirect |
| 6. #26020133 | C2 | semidirect |
| 7. C89×#2140 | C2 | semidirect |
| 13. #19151973 | C4 | semidirect |
| 47. #15667948 | D4 | semidirect |
| 64. #107×C89 | D4 | semidirect |
| 178. #2140 | D89 | semidirect |
| 180. C89 | #13261 | semidirect |
| 233. #107 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151973 | 2 |
| C2×#19151418 | 2 |
| C2×#19151412 | 2 |
| C2×#19151411 | 2 |
| #26021967 | 2 |
| #26020133 | 2 |
| C89×#2140 | 2 |
| #13261 | 89 |