Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
488 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26021242 | C2 | semidirect |
| 5. #26018673 | C2 | semidirect |
| 6. #26018142 | C2 | semidirect |
| 7. C89×#3139 | C2 | semidirect |
| 180. #3139 | D89 | semidirect |
| 185. C89 | #10114 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031635 | 2 |
| #26031177 | 2 |
| #26021242 | 2 |
| #26018843 | 2 |
| #26018673 | 2 |
| #26018142 | 2 |
| C89×#3139 | 2 |
| #10114 | 89 |