Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
636 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 636 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 |
|---|---|---|
| 3. C4×#15667927 | C2 | semidirect |
| 4. #26018371 | C2 | semidirect |
| 5. C4×#100×C89 | C2 | semidirect |
| 7. C22×#13083551 | C4 | semidirect |
| 14. #19151470 | C4 | semidirect |
| 15. #19151453 | C4 | semidirect |
| 17. C4×C22⋊Dic89 | C4 | semidirect |
| 18. #19151386 | C4 | semidirect |
| 69. C23×D89 | C42 | semidirect |
| 85. C22⋊Dic89 | C42 | semidirect |
| 226. C4×#100 | D89 | semidirect |
| 229. C89 | #12622 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022906 | 2 |
| C2×#19151386 | 2 |
| C4×#15667927 | 2 |
| #26018371 | 2 |
| C4×#100×C89 | 2 |
| #12622 | 89 |