Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
218 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 69 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. #26019072 | C2 | semidirect |
| 4. #26018318 | C2 | semidirect |
| 5. #26018223 | C2 | semidirect |
| 7. C89×#1313 | C2 | semidirect |
| 48. Dic356 | M16 | semidirect |
| 109. #1313 | D89 | semidirect |
| 110. C89 | #12080 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022118 | 2 |
| #26019167 | 2 |
| #26019072 | 2 |
| #26018318 | 2 |
| #26018223 | 2 |
| #26018220 | 2 |
| C89×#1313 | 2 |
| #12080 | 89 |