Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
820 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 107 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×#19151384 | C2 | semidirect |
| 3. #26020180 | C2 | semidirect |
| 4. #26018369 | C2 | semidirect |
| 5. C2×#410×C89 | C2 | semidirect |
| 6. C2×#15667980 | C4 | semidirect |
| 8. C22×#13083551 | C4 | semidirect |
| 14. #19151478 | C4 | semidirect |
| 18. #19151461 | C4 | semidirect |
| 71. #99×C89 | D4 | semidirect |
| 270. C2×#410 | D89 | semidirect |
| 275. C89 | #13087 | semidirect |
| 335. #99 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023567 | 2 |
| C2×#19151384 | 2 |
| #26020180 | 2 |
| #26018369 | 2 |
| C2×#410×C89 | 2 |
| #13087 | 89 |