Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
490 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #26018765 | C2 | semidirect |
| 5. #26018763 | C2 | semidirect |
| 6. #26018146 | C2 | semidirect |
| 7. C89×#1300 | C2 | semidirect |
| 10. #19151958 | C4 | semidirect |
| 11. #19151958 | C4 | semidirect |
| 34. #15668012 | C2×C4 | semidirect |
| 35. #15668012 | C2×C4 | semidirect |
| 72. #97×C89 | C2×C4 | semidirect |
| 210. #1300 | D89 | semidirect |
| 211. C89 | #9439 | semidirect |
| 271. #97 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030639 | 2 |
| #26023362 | 2 |
| #26018875 | 2 |
| #26018765 | 2 |
| #26018763 | 2 |
| #26018146 | 2 |
| C89×#1300 | 2 |
| #9439 | 89 |