Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
554 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 101 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. #26021197 | C2 | semidirect |
| 5. #26018751 | C2 | semidirect |
| 6. #26018102 | C2 | semidirect |
| 7. C89×#3249 | C2 | semidirect |
| 196. #3249 | D89 | semidirect |
| 203. C89 | #10195 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031190 | 2 |
| #26030628 | 2 |
| #26021197 | 2 |
| #26021178 | 2 |
| #26018751 | 2 |
| #26018102 | 2 |
| C89×#3249 | 2 |
| #10195 | 89 |