Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
562 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26018201 | C2 | semidirect |
| 4. #26018199 | C2 | semidirect |
| 37. C2×C22⋊Dic89 | C8 | semidirect |
| 81. C22⋊Dic89 | C2×C8 | semidirect |
| 82. C22⋊Dic89 | C2×C8 | semidirect |
| 220. C89 | #11453 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022864 | 2 |
| C2×#19151322 | 2 |
| #26018201 | 2 |
| #26018199 | 2 |
| C2×#323×C89 | 2 |
| #11453 | 89 |