Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
976 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 976 conjugacy classes of subgroups — too many to draw. Only its 183 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. #26019294 | C2 | semidirect |
| 4. #26019192 | C2 | semidirect |
| 5. #26018772 | C2 | semidirect |
| 6. #26018582 | C2 | semidirect |
| 7. C2×#544×C89 | C2 | semidirect |
| 204. C2×#544 | D89 | semidirect |
| 211. C89 | #18326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031054 | 2 |
| #26025732 | 2 |
| #26019294 | 2 |
| #26019192 | 2 |
| #26018772 | 2 |
| #26018582 | 2 |
| C2×#544×C89 | 2 |
| #18326 | 89 |