Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
224 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 119 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. #26018326 | C2 | semidirect |
| 4. #26018324 | C2 | semidirect |
| 53. C16×C89 | M16 | semidirect |
| 95. C89 | #12025 | semidirect |
| 143. C16 | #13083558 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26019015 | 2 |
| #26019011 | 2 |
| #26018326 | 2 |
| #26018324 | 2 |
| C4×M32×C89 | 2 |
| #12025 | 89 |