Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
2286 conjugacy classes of subgroups; only the 443 normal subgroups are shown.
This group has 2286 conjugacy classes of subgroups — too many to draw. Only its 443 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. C2×#19151466 | C2 | semidirect |
| 3. #26018476 | C2 | semidirect |
| 5. C2×#383×C89 | C2 | semidirect |
| 11. C2×C42×D89 | C4 | semidirect |
| 68. C42×C89 | C22⋊C4 | semidirect |
| 109. C2×D89 | #383 | semidirect |
| 123. C2×#383 | D89 | semidirect |
| 126. C89 | #14683 | semidirect |
| 189. C42 | #13083551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C42×D89 | 2 |
| C2×#19151466 | 2 |
| #26018476 | 2 |
| #26018473 | 2 |
| C2×#383×C89 | 2 |
| #14683 | 89 |