Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
600 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 600 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 |
|---|---|---|
| 2. #26020318 | C2 | semidirect |
| 4. #26018099 | C2 | semidirect |
| 73. C22×Dic89 | M16 | semidirect |
| 82. C22⋊Dic89 | M16 | semidirect |
| 201. C89 | #8968 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15667993 | 2 |
| #26020318 | 2 |
| #26018570 | 2 |
| #26018099 | 2 |
| C89×#2973 | 2 |
| #8968 | 89 |