Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
358 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 119 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. #26022025 | C2 | semidirect |
| 5. #26018365 | C2 | semidirect |
| 6. #26018359 | C2 | semidirect |
| 7. C2×#365×C89 | C2 | semidirect |
| 10. #19152014 | C4 | semidirect |
| 140. C2×#365 | D89 | semidirect |
| 145. C89 | #12833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033354 | 2 |
| #26022025 | 2 |
| #26020312 | 2 |
| #26020307 | 2 |
| #26018365 | 2 |
| #26018359 | 2 |
| C2×#365×C89 | 2 |
| #12833 | 89 |