Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
316 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 67 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. #26021941 | C2 | semidirect |
| 3. #26018424 | C2 | semidirect |
| 4. #26018418 | C2 | semidirect |
| 5. C89×#2135 | C2 | semidirect |
| 149. #2135 | D89 | semidirect |
| 153. C89 | #13611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031313 | 2 |
| #26021941 | 2 |
| #26018424 | 2 |
| #26018418 | 2 |
| C89×#2135 | 2 |
| #13611 | 89 |