Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
390 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 63 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. #26031593 | C2 | semidirect |
| 5. #26018263 | C2 | semidirect |
| 6. #26018191 | C2 | semidirect |
| 7. C89×#1348 | C2 | semidirect |
| 136. C2×Dic89 | SD32 | semidirect |
| 181. #1348 | D89 | semidirect |
| 183. C89 | #12159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031593 | 2 |
| #26022183 | 2 |
| #26022180 | 2 |
| #26021564 | 2 |
| #26018263 | 2 |
| #26018191 | 2 |
| C89×#1348 | 2 |
| #12159 | 89 |