Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
542 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26018576 | C2 | semidirect |
| 4. #26018084 | C2 | semidirect |
| 5. C89×#2983 | C2 | semidirect |
| 152. #2983 | D89 | semidirect |
| 157. C89 | #8964 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15668001 | 2 |
| #26018642 | 2 |
| #26018576 | 2 |
| #26018084 | 2 |
| C89×#2983 | 2 |
| #8964 | 89 |