Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
700 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 87 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×#19151365 | C2 | semidirect |
| 3. #26018277 | C2 | semidirect |
| 4. #26018250 | C2 | semidirect |
| 5. C89×#1462 | C2 | semidirect |
| 7. C2×#15667986 | C4 | semidirect |
| 10. #19151534 | C4 | semidirect |
| 12. #19151507 | C4 | semidirect |
| 16. C4×C22⋊Dic89 | C4 | semidirect |
| 23. C22×D356 | C2×C4 | semidirect |
| 32. C2×C4⋊Dic89 | C2×C4 | semidirect |
| 46. #15667919 | C2×C4 | semidirect |
| 47. #15667919 | C2×C4 | semidirect |
| 246. #1462 | D89 | semidirect |
| 249. C89 | #11757 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025183 | 2 |
| C2×#19151365 | 2 |
| #26018277 | 2 |
| #26018250 | 2 |
| C89×#1462 | 2 |
| #11757 | 89 |