Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
568 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 83 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. #26026050 | C2 | semidirect |
| 5. #26020352 | C2 | semidirect |
| 6. #26018159 | C2 | semidirect |
| 7. C89×#1508 | C2 | semidirect |
| 228. #1508 | D89 | semidirect |
| 230. C89 | #9933 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031054 | 2 |
| #26030193 | 2 |
| #26026050 | 2 |
| #26021088 | 2 |
| #26020352 | 2 |
| #26018159 | 2 |
| C89×#1508 | 2 |
| #9933 | 89 |