Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
374 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 3. #26019022 | C2 | semidirect |
| 5. #26018148 | C2 | semidirect |
| 6. #26018147 | C2 | semidirect |
| 7. C89×#1571 | C2 | semidirect |
| 164. #1571 | D89 | semidirect |
| 169. C89 | #8863 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028889 | 2 |
| #26020233 | 2 |
| #26019022 | 2 |
| #26018564 | 2 |
| #26018148 | 2 |
| #26018147 | 2 |
| C89×#1571 | 2 |
| #8863 | 89 |