Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1206 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 1206 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. C2×#19151392 | C2 | semidirect |
| 5. C23×Dic178 | C4 | semidirect |
| 9. C2×#15667999 | C4 | semidirect |
| 13. C22×C4×Dic89 | C4 | semidirect |
| 69. C2×Dic178 | C22⋊C4 | semidirect |
| 87. C4×Dic89 | C22⋊C4 | semidirect |
| 202. C22×C89 | #354 | semidirect |
| 226. C89 | #12694 | semidirect |
| 424. C22 | #19151392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667999 | 2 |
| C2×#19151392 | 2 |
| #26020167 | 2 |
| C89×#1781 | 2 |
| #12694 | 89 |