Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
818 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 818 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×#19151582 | C2 | semidirect |
| 3. C2×#19151384 | C2 | semidirect |
| 4. #26018369 | C2 | semidirect |
| 5. C89×#1782 | C2 | semidirect |
| 7. C2×#15667980 | C4 | semidirect |
| 9. C22×#13083551 | C4 | semidirect |
| 15. #19151478 | C4 | semidirect |
| 19. #19151461 | C4 | semidirect |
| 49. #15667929 | D4 | semidirect |
| 270. #1782 | D89 | semidirect |
| 272. C89 | #13083 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151582 | 2 |
| #26023567 | 2 |
| C2×#19151384 | 2 |
| #26018369 | 2 |
| C89×#1782 | 2 |
| #13083 | 89 |