Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
450 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26028897 | C2 | semidirect |
| 3. #26018843 | C2 | semidirect |
| 4. #26018702 | C2 | semidirect |
| 5. #26018689 | C2 | semidirect |
| 6. #26018088 | C2 | semidirect |
| 7. C89×#1299 | C2 | semidirect |
| 207. #1299 | D89 | semidirect |
| 209. C89 | #9213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030313 | 2 |
| #26028897 | 2 |
| #26018843 | 2 |
| #26018702 | 2 |
| #26018689 | 2 |
| #26018088 | 2 |
| C89×#1299 | 2 |
| #9213 | 89 |