Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
818 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 818 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. #26022609 | C2 | semidirect |
| 4. #26018106 | C2 | semidirect |
| 5. C89×#1463 | C2 | semidirect |
| 10. #19151518 | C4 | semidirect |
| 11. #19151515 | C4 | semidirect |
| 125. C2×C4×C89 | #104 | semidirect |
| 179. #1463 | D89 | semidirect |
| 181. C89 | #9476 | semidirect |
| 317. C2×C4 | #15667938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023587 | 2 |
| #26022609 | 2 |
| #26020195 | 2 |
| #26018106 | 2 |
| C89×#1463 | 2 |
| #9476 | 89 |