Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
2286 conjugacy classes of subgroups; only the 555 normal subgroups are shown.
This group has 2286 conjugacy classes of subgroups — too many to draw. Only its 555 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 |
|---|---|---|
| 1. C2×#19151466 | C2 | semidirect |
| 2. #26018479 | C2 | semidirect |
| 11. C22×C42×C89 | C4 | semidirect |
| 52. C42×C89 | C22⋊C4 | semidirect |
| 78. C22×C89 | #383 | semidirect |
| 98. C89 | #14683 | semidirect |
| 102. C22×C42 | Dic89 | semidirect |
| 146. C42 | C22⋊Dic89 | semidirect |
| 172. C22 | #19151466 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151466 | 2 |
| #26018479 | 2 |
| #26018475 | 2 |
| C23×C42×C89 | 2 |
| #14683 | 89 |